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searching for Irreducible representation 103 found (229 total)

alternate case: irreducible representation

Weyl character formula (3,441 words) [view diff] exact match in snippet view article find links to article

1926b). There is a closely related formula for the character of an irreducible representation of a semisimple Lie algebra. In Weyl's approach to the representation
Chang number (292 words) [view diff] exact match in snippet view article find links to article
In mathematics, the Chang number of an irreducible representation of a simple complex Lie algebra is its dimension modulo 1 + h, where h is the Coxeter
Compact group (4,392 words) [view diff] exact match in snippet view article find links to article
representations of T. (Note that a given irreducible representation of T may occur more than once.) Now, each irreducible representation of T is described by a linear
Immanant (432 words) [view diff] exact match in snippet view article find links to article
and let χλ{\displaystyle \chi _{\lambda }} be the corresponding irreducible representation-theoretic character of the symmetric group Sn{\displaystyle S_{n}}
Itô's theorem (100 words) [view diff] exact match in snippet view article find links to article
the dimension of an irreducible representation of a group must divide the order of that group. Given an irreducible representation V of a finite group
Dual representation (1,638 words) [view diff] exact match in snippet view article find links to article
each irreducible representation does turn out to be isomorphic to the representation. But for the representations of SU(3), the dual of the irreducible representation
Theorem of the highest weight (1,102 words) [view diff] exact match in snippet view article find links to article
weight then states: If V {\displaystyle V} is a finite-dimensional irreducible representation of g {\displaystyle {\mathfrak {g}}} , then V {\displaystyle V}
Gamas's theorem (357 words) [view diff] exact match in snippet view article find links to article
necessary and sufficient conditions for a tensor symmetrized by an irreducible representation of the symmetric group S n {\displaystyle S_{n}} to be zero. It
Θ10 (449 words) [view diff] exact match in snippet view article find links to article
a branch of mathematics, θ10 is a cuspidal unipotent complex irreducible representation of the symplectic group Sp4 over a finite, local, or global field
Representations of classical Lie groups (3,363 words) [view diff] exact match in snippet view article find links to article
groups, their representations are tensor representations. Each irreducible representation is labelled by a Young diagram, which encodes its structure and
McKay graph (1,460 words) [view diff] exact match in snippet view article find links to article
structure of the representation theory of G. Each node represents an irreducible representation of G. If χ i, χ j are irreducible representations of G, then there
Representation theory of SL2(R) (1,803 words) [view diff] exact match in snippet view article
complexified Lie algebra of SL(2, R). The Casimir element acts on any irreducible representation as multiplication by some complex scalar μ2. Thus in the case
Subatomic particle (3,133 words) [view diff] exact match in snippet view article find links to article
particle is a quantum excitation of a field A particle is an irreducible representation of the Poincaré group A particle is an observed thing Subatomic
Littelmann path model (2,117 words) [view diff] exact match in snippet view article find links to article
Seshadri and Lakshmibai, Littelmann's path model associates to each irreducible representation a rational vector space with basis given by paths from the origin
Fuzzy sphere (580 words) [view diff] exact match in snippet view article find links to article
{\displaystyle J_{a},~a=1,2,3} that form a basis for the j dimensional irreducible representation of the Lie algebra su(2). They satisfy the relations [ J a , J
Yoshimine sort (1,277 words) [view diff] exact match in snippet view article find links to article
to the C1{\displaystyle C_{1}} point group which has only one irreducible representation, then the permutational symmetry of the integrals indices is the
Plasmonic nanoparticles (1,775 words) [view diff] exact match in snippet view article find links to article
distribution of the electrons and alter the mulliken term symbol for the irreducible representation. Changing the geometry of the nanoparticles can be used to manipulate
Representation theory of diffeomorphism groups (833 words) [view diff] exact match in snippet view article find links to article
the space of sections of the tensor and jet bundles would be an irreducible representation and we often look at a subrepresentation of them. We can study
Special linear Lie algebra (1,775 words) [view diff] exact match in snippet view article find links to article
in an irreducible representation, we have a "highest" eigenvector of "h", on which "e" acts by zero. The basis of the irreducible representation is generated
Fischer group Fi22 (866 words) [view diff] exact match in snippet view article find links to article
vectors is a 77-dimensional irreducible representation. The perfect triple cover of Fi22 has an irreducible representation of dimension 27 over the field
Jacquet module (369 words) [view diff] exact match in snippet view article find links to article
general linear group GL(2), the Jacquet module of an admissible irreducible representation has dimension at most two. If the dimension is zero, then the
List of finite-dimensional Nichols algebras (1,993 words) [view diff] exact match in snippet view article find links to article
conjugacy class [ g ] ⊂ G {\displaystyle [g]\subset G} and an irreducible representation χ {\displaystyle \chi } of the centralizer Cent ⁡ ( g ) {\displaystyle
Harish-Chandra module (376 words) [view diff] exact match in snippet view article find links to article
K)}-module X is isomorphic to the Harish-Chandra module of an irreducible representation of G on a Hilbert space. Such representations are admissible,
Frobenius formula (676 words) [view diff] exact match in snippet view article find links to article
Let χλ{\displaystyle \chi _{\lambda }} be the character of an irreducible representation of the symmetric group Sn{\displaystyle S_{n}} corresponding to
Representation ring (838 words) [view diff] exact match in snippet view article find links to article
1-dimensional alternating representation and Y the 2-dimensional irreducible representation of S3. Any representation defines a character χ:G → C. Such a
Permutation representation (686 words) [view diff] no match in snippet view article find links to article
Media. ISBN 9781468401288. https://mathoverflow.net/questions/286393/how-do-i-know-if-an-irreducible-representation-is-a-permutation-representation v t e
Fischer group Fi23 (547 words) [view diff] exact match in snippet view article find links to article
representation has dimension 782{\displaystyle 782}. The group has an irreducible representation of dimension 253 over the field with 3 elements. Conway and Norton
Jones polynomial (2,284 words) [view diff] exact match in snippet view article find links to article
Reshetikhin–Turaev invariant associated with the (N+1){\displaystyle (N+1)}-irreducible representation of the quantum group Uq(sl2){\displaystyle U_{q}({\mathfrak {sl}}_{2})}
Polarization mode dispersion (685 words) [view diff] exact match in snippet view article find links to article
requires a core whose symmetry group admits a two-dimensional irreducible representation. For example, a square or equilateral-triangle core would also
Polarization mode dispersion (685 words) [view diff] exact match in snippet view article find links to article
requires a core whose symmetry group admits a two-dimensional irreducible representation. For example, a square or equilateral-triangle core would also
Coherent states in mathematical physics (5,573 words) [view diff] exact match in snippet view article find links to article
a locally compact group and suppose that it has a continuous, irreducible representation U{\displaystyle U} on a Hilbert space H{\displaystyle {\mathfrak
Harmonic analysis (1,219 words) [view diff] exact match in snippet view article find links to article
Peter–Weyl theorem explains how one may get harmonics by choosing one irreducible representation out of each equivalence class of representations. This choice
Quantum group (4,637 words) [view diff] exact match in snippet view article find links to article
multiplicities of the weights are equal to their multiplicities in an irreducible representation of U(G) with equal highest weight. If the highest weight is dominant
Demazure module (802 words) [view diff] exact match in snippet view article find links to article
maximal length of W then the Demazure module is the whole of the irreducible representation V. Demazure modules can be defined in a similar way for highest
Knizhnik–Zamolodchikov equations (2,839 words) [view diff] exact match in snippet view article find links to article
above. When v is in the lowest energy subspace for L0 on Hk, an irreducible representation of g{\displaystyle {\mathfrak {g}}}, the operator Φ(v, w) is called
Type II string theory (1,012 words) [view diff] exact match in snippet view article find links to article
sectors respectively. The numbers denote the dimension of the irreducible representation and equivalently the number of components of the corresponding
Kähler identities (4,200 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\mathfrak {sl}}(2,\mathbb {C} )} .: Ch V §3  Any such irreducible representation comes with a primitive element, which is an element α {\displaystyle
Sudhansu Datta Majumdar (1,938 words) [view diff] exact match in snippet view article find links to article
an irreducible representation of SU(3). The forms of the new operators made apparent the fact that the basis states of an irreducible representation of
Clifford theory (1,002 words) [view diff] exact match in snippet view article find links to article
subgroup N of finite index: Theorem. Let π: G → GL(n,K) be an irreducible representation with K a field. Then the restriction of π to N breaks up into
W-algebra (5,154 words) [view diff] exact match in snippet view article find links to article
Rd{\displaystyle R_{d}} is the d{\displaystyle d}-dimensional irreducible representation of sl2{\displaystyle {\mathfrak {sl}}_{2}}. The trivial partition
27 (number) (2,438 words) [view diff] exact match in snippet view article
non-strict group of Lie type T{\displaystyle \mathrm {T} } (with an irreducible representation that is twice that of F4{\displaystyle \mathrm {F_{4}} } in 104
Mathieu group M11 (931 words) [view diff] exact match in snippet view article find links to article
The permutation representation on 11 points gives a complex irreducible representation in 10 dimensions. This is the smallest possible dimension of a
Fischer group Fi24 (628 words) [view diff] exact match in snippet view article find links to article
1-dimensional invariant subspaces and quotient spaces, giving an irreducible representation of dimension 781 over the field with 3 elements. Conway and Norton
Garnir relations (876 words) [view diff] exact match in snippet view article find links to article
one has the Specht module Vλ. In characteristic 0, this is an irreducible representation of the symmetric group Sn. One can construct Vλ explicitly in
Nahm equations (887 words) [view diff] exact match in snippet view article find links to article
residues of T1,T2,T3{\displaystyle T_{1},T_{2},T_{3}} form an irreducible representation of the group SU(2). There is a natural equivalence between the
Geometric quantization (1,612 words) [view diff] exact match in snippet view article find links to article
geometric quantization and the resulting Hilbert space carries an irreducible representation of SU(2). In the case that the area of the sphere is 2πℏ{\displaystyle
Frobenius characteristic map (2,092 words) [view diff] exact match in snippet view article find links to article
\quad f\in R^{n}.} In particular, if f {\displaystyle f} is an irreducible representation, then ch ⁡ ( f ) {\displaystyle \operatorname {ch} (f)} is a Schur
Molecular orbital diagram (4,966 words) [view diff] exact match in snippet view article find links to article
an irreducible representation. Carbon dioxide’s molecular orbitals are made by the linear combination of atomic orbitals of the same irreducible representation
Discrete series representation (1,359 words) [view diff] exact match in snippet view article find links to article
character formula, with v = λ + ρ for λ the highest weight of the irreducible representation (where the product is over roots α having positive inner product
Deligne–Lusztig theory (3,998 words) [view diff] exact match in snippet view article find links to article
the length of w) so this cohomology group gives a model for the irreducible representation. In general it is possible for more than one cohomology group
E7 (mathematics) (2,577 words) [view diff] exact match in snippet view article
of the simply connected form of E7. There exist non-isomorphic irreducible representation of dimensions 1903725824, 16349520330, etc. The fundamental representations
Haboush's theorem (1,094 words) [view diff] exact match in snippet view article find links to article
finite field of order q.) The Steinberg representation is an irreducible representation of G(Fq) and therefore of G(K), and for r large enough it has
Spin (physics) (9,941 words) [view diff] exact match in snippet view article
covering group of SO(3), which is SU(2). There is one n-dimensional irreducible representation of SU(2) for each dimension, though this representation is n-dimensional
Bargmann–Wigner equations (2,325 words) [view diff] exact match in snippet view article find links to article
0)}\oplus D_{r}^{(0,1/2)}\right]\,.} where each Dr is an irreducible representation. This representation does not have definite spin unless j equals
Cartan subalgebra (1,980 words) [view diff] exact match in snippet view article find links to article
α∈Φ+{\displaystyle \alpha \in \Phi ^{+}}, there exists a unique irreducible representation L+(λ){\displaystyle L^{+}(\lambda )}. This means the root system
Weyl–Brauer matrices (1,565 words) [view diff] exact match in snippet view article find links to article
split a spinor into a pair of Weyl spinors, and spinors form an irreducible representation of the spin group. As in the even case, it is possible to identify
Lie group (9,356 words) [view diff] exact match in snippet view article find links to article
triangular matrices of some rank, and any finite-dimensional irreducible representation of such a group is 1-dimensional. Solvable groups are too messy
Affine group (2,297 words) [view diff] exact match in snippet view article find links to article
p(p-1)=p-1+\chi _{p}^{2}\,,} hence χp = p − 1 is the dimension of the last irreducible representation. Finally using the orthogonality of irreducible representations
Jacobson radical (2,878 words) [view diff] no match in snippet view article find links to article
theorem and the fact that for a C*-algebra, a topologically irreducible *-representation on a Hilbert space is algebraically irreducible, so that its
100,000 (3,603 words) [view diff] exact match in snippet view article find links to article
dimensions 196,883 = the dimension of the smallest nontrivial irreducible representation of the Monster group 196,884 = the coefficient of q in the Fourier
Kostka number (1,137 words) [view diff] exact match in snippet view article find links to article
weight space corresponding to μ{\displaystyle \mu } in the unitary irreducible representation Uλ{\displaystyle U_{\lambda }} (where we require μ{\displaystyle
Binary icosahedral group (1,683 words) [view diff] exact match in snippet view article find links to article
a 4-dimensional representation (its usual lowest-dimensional irreducible representation as the full symmetries of the (n−1){\displaystyle (n-1)}-simplex)
Representation on coordinate rings (672 words) [view diff] exact match in snippet view article find links to article
X is called multiplicity-free (or spherical variety) if every irreducible representation of G appears at most one time in the coordinate ring; i.e., dim
Circular dichroism (3,839 words) [view diff] exact match in snippet view article find links to article
{\widehat {M}}_{\mathrm {(mag.dipole)} }}) must transform as the same irreducible representation. Cn{\displaystyle \mathrm {C} _{n}} and Dn{\displaystyle \mathrm
Weight (representation theory) (3,204 words) [view diff] exact match in snippet view article
dominant, algebraically integral element is the highest weight of an irreducible representation. The last point is the most difficult one; the representations
Antisymmetrizer (2,506 words) [view diff] no match in snippet view article find links to article
{(−1)π}{\displaystyle \{(-1)^{\pi }\}} forms a one-dimensional (and hence irreducible) representation of the permutation group known as the antisymmetric representation
Chebotarev's density theorem (2,050 words) [view diff] exact match in snippet view article find links to article
and degree d. Take ρ{\displaystyle \rho } to be a nontrivial irreducible representation of G of degree n, and take f(ρ){\displaystyle {\mathfrak {f}}(\rho
Nichols algebra (5,008 words) [view diff] exact match in snippet view article find links to article
corresponds to Conjugacy class of the group (together with an irreducible representation of the centralizer of g). An arbitrary Yetter–Drinfeld module
Conical intersection (1,869 words) [view diff] exact match in snippet view article find links to article
between two electronic states carrying the same multidimensional irreducible representation. For example, intersections between a pair of E states at a geometry
Configuration state function (1,665 words) [view diff] exact match in snippet view article find links to article
group product table has to be used to find the product of the irreducible representation of all N{\displaystyle N} orbitals. couple the total spins of
Gaudin model (2,036 words) [view diff] exact match in snippet view article find links to article
Denote by Vλ{\displaystyle V_{\lambda }} the finite-dimensional irreducible representation of g{\displaystyle {\mathfrak {g}}} corresponding to the dominant
Chern–Simons theory (3,482 words) [view diff] exact match in snippet view article find links to article
attention to irreducible representations R. More concretely, given an irreducible representation R and a loop K in M, one may define the Wilson loop WR(K){\displaystyle
Ali Chamseddine (1,382 words) [view diff] exact match in snippet view article find links to article
Riemannian Spin 4-manifold with quantized volume appears as an irreducible representation of the two-sided commutation relations in dimensions four with
Super-Poincaré algebra (2,621 words) [view diff] exact match in snippet view article find links to article
(0, 1⁄2) respectively for these representations. The general irreducible representation is then (m, n), where m, n are half-integral and correspond physically
Lie group–Lie algebra correspondence (4,464 words) [view diff] exact match in snippet view article find links to article
rotation group SO(3), which is not simply connected. There is one irreducible representation of the Lie algebra in each dimension, but only the odd-dimensional
Prehomogeneous vector space (1,712 words) [view diff] exact match in snippet view article find links to article
it is natural to study the irreducible PVS (i.e., when V is an irreducible representation of G). In this case, a theorem of Élie Cartan shows that G ≤ GL(V)
Wigner–Weyl transform (2,960 words) [view diff] exact match in snippet view article find links to article
eiaQ{\displaystyle e^{iaQ}} and eibP{\displaystyle e^{ibP}} constitute an irreducible representation of the Weyl relations, so that the Stone–von Neumann theorem (guaranteeing
Cambridge 105 (1,902 words) [view diff] case mismatch in snippet view article find links to article
Road in Cambridge. Karl presented a regular music show called Irreducible Representation whose reputation grew until others offered to contribute or present
Classification of Clifford algebras (2,337 words) [view diff] exact match in snippet view article find links to article
⊕ End(CN/2) and therefore decomposes to the direct sum of two irreducible representation spaces Δ+ n ⊕ Δ− n, each isomorphic to CN/2. A left-handed (respectively
Mass (9,960 words) [view diff] exact match in snippet view article find links to article
spectroscopy. In relativistic quantum mechanics, mass is one of the irreducible representation labels of the Poincaré group. In everyday usage, mass and "weight"
Kostant's convexity theorem (1,862 words) [view diff] exact match in snippet view article find links to article
the Weyl group polytope defined by λ are those appearing in the irreducible representation of K with highest weight λ. An argument with lowering operators
Bloch's theorem (5,337 words) [view diff] exact match in snippet view article find links to article
m_{1}}{L_{1}}}} The wave vector k1{\displaystyle k_{1}} identify the irreducible representation in the same manner as m1{\displaystyle m_{1}}, and L1{\displaystyle
Root of unity (5,666 words) [view diff] exact match in snippet view article find links to article
a primitive nth root of unity. The nth roots of unity form an irreducible representation of any cyclic group of order n. The orthogonality relationship
Arthur–Selberg trace formula (2,147 words) [view diff] exact match in snippet view article find links to article
of M(Q,γ)\M(A,γ) aM(π) is related to the multiplicity of the irreducible representation π in L2(M(Q)\M(A)) IM(γ,f){\displaystyle \displaystyle I_{M}(\gamma
Semisimple Lie algebra (5,432 words) [view diff] exact match in snippet view article find links to article
g{\displaystyle {\mathfrak {g}}}-module (a finite-dimensional irreducible representation). This is especially the case when g{\displaystyle {\mathfrak
Maass wave form (7,750 words) [view diff] exact match in snippet view article find links to article
most difficult problems in the theory of automorphic forms. An irreducible representation π{\displaystyle \pi } of the group GA{\displaystyle G_{\mathbb
Invariant of a binary form (2,346 words) [view diff] exact match in snippet view article find links to article
degree n correspond to taking V to be the (n + 1)-dimensional irreducible representation, and covariants correspond to taking V to be the sum of the irreducible
Lie algebra representation (4,193 words) [view diff] exact match in snippet view article find links to article
{0}{\displaystyle \{0\}}. The term simple module is also used for an irreducible representation. Let g{\displaystyle {\mathfrak {g}}} be a Lie algebra. Let V
Weyl's theorem on complete reducibility (2,447 words) [view diff] exact match in snippet view article find links to article
multiple c λ {\displaystyle c_{\lambda }} of the identity in the irreducible representation of g {\displaystyle {\mathfrak {g}}} with highest weight λ {\displaystyle
Issai Schur (3,931 words) [view diff] exact match in snippet view article find links to article
n{\displaystyle n} parts. Moreover Schur showed that the character of an irreducible representation of type λ{\displaystyle \lambda } is given by a certain symmetric
Landau theory (3,851 words) [view diff] exact match in snippet view article find links to article
parameter that embodies the distortion needs to transform as a single irreducible representation (irrep) of the parent symmetry The irrep should not contain a
Oscillator representation (19,823 words) [view diff] exact match in snippet view article find links to article
Neumann theorem: the Schrödinger representation is the unique irreducible representation of the Weyl commutation relations on a Hilbert space. Given U
Littlewood–Richardson rule (3,553 words) [view diff] exact match in snippet view article find links to article
Grassmannian corresponding to μ. cν λμ   is the number of times the irreducible representation Vλ ⊗ Vμ of the product of symmetric groups S|λ| × S|μ| appears
Clifford algebra (8,652 words) [view diff] exact match in snippet view article find links to article
since the pin group is generated by unit vectors, all of its irreducible representation are induced in this manner. Thus the two representations coincide
Joos–Weinberg equation (1,998 words) [view diff] exact match in snippet view article find links to article
..[αjβj] of B[αβ] decomposes into a finite series of Lorentz-irreducible representation spaces according to ⨂i=1j(Di(1,0)⊕Di(0,1))→D(j,0)⊕D(0,j)⊕D(j,j)⊕⋯⊕D(jk
Mathieu group M24 (2,932 words) [view diff] exact match in snippet view article find links to article
is the sum of the trivial representation and a 23-dimensional irreducible representation.[citation needed] M24 has two rank 3 permutation representations:
Fourier transform (20,270 words) [view diff] exact match in snippet view article find links to article
are rows of vectors such that each row is the character of one irreducible representation of G, and these vectors form an orthonormal basis of the space
Feynman diagram (14,939 words) [view diff] exact match in snippet view article find links to article
single-particle states: they are a collection of states that form an irreducible representation of the Poincaré group. Single particle states describe an object
Asım Orhan Barut (3,801 words) [view diff] case mismatch in snippet view article find links to article
Amplitude in the Left Half-Plane of Complex Angular Momentum 1966 on Irreducible Representation of a Class of Algebras and Related Projective Representations
List of character tables for chemically important 3D point groups (1,263 words) [view diff] exact match in snippet view article find links to article
and rotations about them transform as the A{\displaystyle A} irreducible representation. The families of groups with these symmetries have only one rotation
Capelli's identity (5,562 words) [view diff] exact match in snippet view article find links to article
GLn×GLm{\displaystyle GL_{n}\times GL_{m}} is multiplicity free, that is each irreducible representation occurs only one time. One easily observe the strong similarity
Moy–Prasad filtration (4,086 words) [view diff] exact match in snippet view article find links to article
finite-index normal subgroup. Let ρ {\displaystyle \rho } be an irreducible representation of G ( k ) x {\displaystyle G(k)_{x}} whose restriction to G (
744 (number) (27,080 words) [view diff] exact match in snippet view article
dim⁡248{\displaystyle \operatorname {dim} 248}) whose values themselves embed irreducible representation of e8{\displaystyle {\mathfrak {e_{8}}}}.: p.6  In turn, exceptional