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searching for Trivial representation 46 found (76 total)

Irreducible representation (2,824 words) [view diff] exact match in snippet view article find links to article

groups G {\displaystyle G} have a zero-dimensional, irreducible trivial representation by mapping all group elements to the identity transformation. Any

Springer correspondence (847 words) [view diff] exact match in snippet view article find links to article

occurs exactly once in the correspondence, although φ may be a non-trivial representation. The Springer correspondence has been described explicitly in all

Sum of two squares theorem (835 words) [view diff] exact match in snippet view article find links to article

second representation for c 2 {\displaystyle c^{2}} beyond the trivial representation c 2 + 0 2 {\displaystyle c^{2}+0^{2}} . The prime decomposition

Quasirandom group (1,803 words) [view diff] exact match in snippet view article find links to article

(\Gamma _{n})} are quasirandom. The dimension of the smallest non-trivial representation of Γ n {\displaystyle \Gamma _{n}} is unbounded. The size of the

Representation theory of the symmetric group (2,840 words) [view diff] exact match in snippet view article find links to article

symmetric group has a one-dimensional representation called the trivial representation, where every element acts as the one by one identity matrix. For

Deligne–Lusztig theory (4,066 words) [view diff] exact match in snippet view article find links to article

representation RθT contains the trivial representation if and only if θ=1 (in which case the trivial representation occurs exactly once). The representation

Multiplet (1,702 words) [view diff] exact match in snippet view article find links to article

commonly denoted ϕ {\displaystyle \phi } , which transform in the trivial representation, vector fields A μ {\displaystyle A_{\mu }} (strictly, this might

Alternating polynomial (1,171 words) [view diff] exact match in snippet view article find links to article

representations: the trivial representation and the sign representation. The symmetric polynomials are the trivial representation, and the alternating

Quaternion group (3,716 words) [view diff] exact match in snippet view article find links to article

representations over the complex numbers, with dimensions 1, 1, 1, 1, 2: Trivial representation. Sign representations with i, j, k-kernel: Q8 has three maximal

Frobenius–Schur indicator (1,461 words) [view diff] exact match in snippet view article find links to article

where W triv {\displaystyle W_{\text{triv}}} is the trivial representation. To see this, note that the term χ ( g 2 ) {\displaystyle \chi (g^{2})}

Triplet state (1,096 words) [view diff] exact match in snippet view article find links to article

4-dimensional representation decomposes into the sum of a one-dimensional trivial representation (singlet, a scalar, spin zero) and a three-dimensional representation

Amenable group (3,232 words) [view diff] exact match in snippet view article find links to article

contained in the left regular representation λ on L2(G). Trivial representation. The trivial representation of G is weakly contained in the left regular representation

Unipotent representation (374 words) [view diff] exact match in snippet view article find links to article

the decomposition of the Deligne–Lusztig characters R1 T of the trivial representation 1 of a torus T . They were classified by Lusztig (1978, 1979). Some

Shellshock: Nam '67 (1,051 words) [view diff] exact match in snippet view article find links to article

of war as tasteless. Eurogamer also noted that the game was "a trivial representation of a bloody conflict for our personal entertainment" but thought

Artin conductor (935 words) [view diff] exact match in snippet view article find links to article

character of the regular representation and 1 is the character of the trivial representation. The Swan character is the character of a representation of G. Swan (1963)

Polite number (2,113 words) [view diff] exact match in snippet view article find links to article

polite representations and odd factors (including in this case the trivial representation n = n and the trivial odd factor 1). If a polite representation

Representation theory of finite groups (21,294 words) [view diff] exact match in snippet view article find links to article

denote the degree of a representation ρ . {\displaystyle \rho .} The trivial representation is given by ρ ( s ) = Id {\displaystyle \rho (s)={\text{Id}}} for

Linear independence (4,400 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbf {0} } as a linear combination of its vectors is the trivial representation in which all the scalars a i {\textstyle a_{i}} are zero. Even more

Character group (1,515 words) [view diff] exact match in snippet view article find links to article

characters. These are denoted by f1, ..., fn. The function f1 is the trivial representation, which is given by f 1 ( g ) = 1 {\displaystyle f_{1}(g)=1} for

Beilinson–Bernstein localization (687 words) [view diff] exact match in snippet view article find links to article

finite dimensional sl2 representation on which Ω acts by zero is the trivial representation k, which is sent to the constant sheaf, i.e. the ring of functions

Mathieu group M23 (804 words) [view diff] exact match in snippet view article find links to article

corresponding to the permutation action on 23 points decomposes into the trivial representation and a 22-dimensional representation. The 22-dimensional representation

Lie algebra cohomology (2,251 words) [view diff] exact match in snippet view article find links to article

g {\displaystyle U{\mathfrak {g}}} -module). Considering R as a trivial representation of g {\displaystyle {\mathfrak {g}}} , one defines the cohomology

Parity (physics) (5,164 words) [view diff] exact match in snippet view article

{\text{O}}(3),} scalars: ρ ( R ) = 1 {\displaystyle \rho (R)=1} , the trivial representation pseudoscalars: ρ ( R ) = det ( R ) {\displaystyle \rho (R)=\det(R)}

Semisimple representation (4,081 words) [view diff] exact match in snippet view article find links to article

semisimple decomposition, need not be unique; for example, for a trivial representation, simple representations are one-dimensional vector spaces and thus

Whitehead's lemma (Lie algebra) (1,180 words) [view diff] exact match in snippet view article

))=\operatorname {tr} (\pi (c))=0} ; that is, π {\displaystyle \pi } is a trivial representation. Since g = [ g , g ] {\displaystyle {\mathfrak {g}}=[{\mathfrak

Anatoly Karatsuba (9,409 words) [view diff] exact match in snippet view article find links to article

described as the p-adic field being a C2 field; in other words non-trivial representation of zero would occur if the number of variables was at least d2.

E8 (mathematics) (6,100 words) [view diff] exact match in snippet view article

group E8 is unique among simple compact Lie groups in that its non-trivial representation of smallest dimension is the adjoint representation (of dimension

BRST quantization (9,464 words) [view diff] exact match in snippet view article find links to article

}} , and the ghost c {\displaystyle c} itself) which carry a non-trivial representation of the gauge group. While the Lagrangian density isn't BRST invariant

Von Neumann algebra (5,917 words) [view diff] exact match in snippet view article find links to article

of a countable discrete group with Kazhdan's property (T) (the trivial representation is isolated in the dual space), such as SL(3,Z), has a countable

Hopf algebra (4,397 words) [view diff] exact match in snippet view article find links to article

∈ M, n ∈ N and Δ(a) = (a1, a2). Furthermore, we can define the trivial representation as the base field K with a ( m ) := ϵ ( a ) m {\displaystyle a(m):=\epsilon

Tannaka–Krein duality (1,422 words) [view diff] exact match in snippet view article find links to article

transformation is tensor-preserving if it is the identity map on the trivial representation of G, and if it preserves tensor products in the sense that τ V

Dihedral group of order 6 (2,657 words) [view diff] exact match in snippet view article find links to article

unitary representations, which we will call I {\displaystyle I} (the trivial representation), ρ 1 {\displaystyle \rho _{1}} and ρ 2 {\displaystyle \rho _{2}}

Hidden subgroup problem (2,031 words) [view diff] exact match in snippet view article find links to article

g'\end{cases}}} We let χ g ′ {\displaystyle \chi _{g'}} be the trivial representation, which maps all inputs to 1 {\displaystyle 1} , to get ∑ h ∈ H χ

Conway group (2,300 words) [view diff] exact match in snippet view article find links to article

matrices whose denominators are all divisors of 8. The smallest non-trivial representation of Co0 over any field is the 24-dimensional one coming from the

Linear algebraic group (6,000 words) [view diff] exact match in snippet view article find links to article

additive group G a {\displaystyle \mathbf {G} _{\mathrm {a} }} is the trivial representation. So every representation of G a {\displaystyle \mathbf {G} _{\mathrm

Restricted representation (3,061 words) [view diff] exact match in snippet view article find links to article

context of his theory of dual pairs. The special case where σ is the trivial representation of H was first used extensively by Hua in his work on the Szegő

Wigner–Eckart theorem (2,705 words) [view diff] no match in snippet view article find links to article

representations, two spin-1 representations, and a spin-0 (i.e. trivial) representation. The nonzero matrix elements can only come from the spin-0 subspace

Arthur–Selberg trace formula (2,258 words) [view diff] exact match in snippet view article find links to article

formula for the character of the representation induced from the trivial representation of a subgroup of finite index. In the compact case, which is essentially

Representations of classical Lie groups (3,748 words) [view diff] exact match in snippet view article find links to article

C ) {\displaystyle GL(n,\mathbb {C} )} Dimension Young diagram Trivial representation 1 {\displaystyle 1} ( ) {\displaystyle ()} Determinant representation

Weyl's theorem on complete reducibility (2,465 words) [view diff] no match in snippet view article find links to article

quotient V / W {\displaystyle V/W} is a one dimensional—and therefore trivial—representation of g {\displaystyle {\mathfrak {g}}} , the action of C {\displaystyle

Congruence subgroup (4,782 words) [view diff] exact match in snippet view article find links to article

) {\displaystyle L^{2}(G/\Gamma )} being bounded away from the trivial representation (in the Fell topology on the unitary dual of ⁠ G {\displaystyle

Mathieu group M24 (3,022 words) [view diff] exact match in snippet view article find links to article

linear representation over the complex numbers is the sum of the trivial representation and a 23-dimensional irreducible representation.[citation needed]

Homotopy Lie algebra (2,645 words) [view diff] exact match in snippet view article find links to article

of vectors and V 1 = R {\displaystyle V_{1}=\mathbb {R} } is the trivial representation. Then, there is a higher bracket l 3 {\displaystyle l_{3}} given

Vertex operator algebra (8,938 words) [view diff] exact match in snippet view article find links to article

n, with commutation relations [bn,bm]=n δn,–m), induced by the trivial representation of the subalgebra spanned by bn, n ≥ 0. The Fock space V0 can be

Poisson manifold (12,662 words) [view diff] exact match in snippet view article find links to article

groups of T ∗ M {\displaystyle T^{*}M} with coefficients in the trivial representation; the modular class of a Poisson manifold coincides with the modular

Ordinal collapsing function (12,608 words) [view diff] exact match in snippet view article find links to article

possible ε {\displaystyle \varepsilon } -number base which gives a non-trivial representation. Beyond this, we may need to express ordinals beyond Ω {\displaystyle