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searching for Maximal torus 29 found (75 total)

alternate case: maximal torus

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

characters of an F-stable maximal torus, which is irreducible (up to sign) when the character is in general position. When the maximal torus is split, these representations
Diagonalizable group (244 words) [view diff] exact match in snippet view article find links to article
complex torus). A k-torus is a torus defined over k. The centralizer of a maximal torus is called a Cartan subgroup. Diagonal subgroup Borel, A. Linear algebraic
Hermitian symmetric space (7,418 words) [view diff] exact match in snippet view article find links to article
compact Lie groups by maximal closed connected subgroups which contain a maximal torus and have center isomorphic to the circle group. There is a complete
Complexification (Lie group) (7,216 words) [view diff] exact match in snippet view article
element fixed by σ, let S be a maximal torus in CG(x)σ and let T be the identity component of CG(x, S). Then T is a maximal torus in G containing x and S. It
Siegel upper half-space (692 words) [view diff] exact match in snippet view article find links to article
(n)=\mathrm {Sp} (2g,\mathbb {R} )\cap \mathrm {GL} (g,\mathbb {C} )} is the maximal torus. Since the isometry group of a symmetric space G / K {\displaystyle
Root datum (543 words) [view diff] exact match in snippet view article find links to article
over an algebraically closed field K {\displaystyle K} with a split maximal torus T {\displaystyle T} then its root datum is a quadruple ( X ∗ , Φ , X
Bruhat decomposition (793 words) [view diff] exact match in snippet view article find links to article
{\displaystyle W} is a Weyl group of G {\displaystyle G} corresponding to a maximal torus of B {\displaystyle B} . The Bruhat decomposition of G {\displaystyle
Linear algebraic group (6,000 words) [view diff] exact match in snippet view article find links to article
any maximal torus T in a linear algebraic group G over a field k, Grothendieck showed that T k ¯ {\displaystyle T_{\overline {k}}} is a maximal torus in
Blattner's conjecture (890 words) [view diff] exact match in snippet view article find links to article
Harish-Chandra character formula for a discrete series representation to the maximal torus of a maximal compact group. The problem in proving the Blattner formula
An Exceptionally Simple Theory of Everything (2,339 words) [view diff] exact match in snippet view article find links to article
orthogonal circles that do not twist around each other, and so form a maximal torus within the Lie group, corresponding to a collection of R mutually-commuting
Algebraic torus (3,967 words) [view diff] exact match in snippet view article find links to article
{\displaystyle F} then: its rank (or absolute rank) is the rank of a maximal torus subgroup in G {\displaystyle \mathbf {G} } (note that all maximal tori
Quasi-split group (153 words) [view diff] exact match in snippet view article find links to article
Galois group on a Dynkin diagram. All split groups (those with a split maximal torus) are quasi-split. These correspond to quasi-split groups where the action
Satake isomorphism (863 words) [view diff] exact match in snippet view article find links to article
\mathbb {C} } . Let T ( C ) {\displaystyle T(\mathbb {C} )} be the maximal torus of G ( C ) {\displaystyle G(\mathbb {C} )} , W {\displaystyle W} be
Representation ring (977 words) [view diff] exact match in snippet view article find links to article
Lie group, R(G) is isomorphic to the subring of R(T) (where T is a maximal torus) consisting of those class functions that are invariant under the action
(B, N) pair (992 words) [view diff] exact match in snippet view article
parabolic subgroup of G, and N = N(K), where N is the normalizer of a split maximal torus contained in P. In particular, any finite group of Lie type has the
Langlands dual group (936 words) [view diff] exact match in snippet view article find links to article
root datum (X*, Δ,X*, Δv), where X* is the lattice of characters of a maximal torus, X* the dual lattice (given by the 1-parameter subgroups), Δ the roots
Langlands–Shahidi method (1,570 words) [view diff] exact match in snippet view article find links to article
group of G. When G is the special linear group SL(2), and M = T is the maximal torus of diagonal matrices, then π is a Größencharakter and the corresponding
Satake diagram (912 words) [view diff] exact match in snippet view article find links to article
the reals. We let S be a maximal split torus in G, and take T to be a maximal torus containing S defined over the separable algebraic closure K of k. Then
Poisson–Lie group (1,124 words) [view diff] exact match in snippet view article find links to article
above. Let G {\displaystyle G} be any semisimple Lie group. Choose a maximal torus T ⊂ G {\displaystyle T\subset G} and a choice of positive roots. Let
Haboush's theorem (1,094 words) [view diff] exact match in snippet view article find links to article
The structure of the representation A(G) is given as follows. Pick a maximal torus T of G, and let it act on A(G) by right translations (so that it commutes
Equivariant sheaf (1,463 words) [view diff] exact match in snippet view article find links to article
Let G be a semisimple algebraic group, and λ:H→C a character on a maximal torus H. It extends to a Borel subgroup λ:B→C, giving a one dimensional representation
Pseudo-reductive group (1,102 words) [view diff] exact match in snippet view article find links to article
the ground field) is non-reduced; such examples exist with a split maximal torus and an irreducible non-reduced root system of any positive rank over
Chow variety (2,177 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \operatorname {Gr} (2,\mathbb {C} ^{n})} by the standard maximal torus. Picard variety GIT quotient The notation for Chow varieties is not
Littelmann path model (2,147 words) [view diff] exact match in snippet view article find links to article
corresponds to a maximal rank closed subgroup, i.e. one containing a maximal torus. Weyl 1953, p. 230,312. The "Brauer-Weyl rules" for restriction to maximal
Weyl character formula (3,622 words) [view diff] exact match in snippet view article find links to article
be a compact, connected Lie group and let T {\displaystyle T} be a maximal torus in K {\displaystyle K} . Let Π {\displaystyle \Pi } be an irreducible
Glossary of algebraic geometry (12,496 words) [view diff] exact match in snippet view article find links to article
over a field k {\displaystyle k} is split-reductive if and only if a maximal torus T ⊆ G {\displaystyle T\subseteq G} defined over k {\displaystyle k}
Glossary of representation theory (5,011 words) [view diff] exact match in snippet view article find links to article
integration formula says: given a compact connected Lie group G with a maximal torus T, there exists a real continuous function u on T such that for every
K-stability of Fano varieties (9,391 words) [view diff] exact match in snippet view article find links to article
configurations which are equivariant with respect to the action of a maximal torus T ⊂ Aut ⁡ ( X ) {\displaystyle T\subset \operatorname {Aut} (X)} , and
Mutation (Jordan algebra) (15,817 words) [view diff] exact match in snippet view article
_{2}&0\\0&\zeta _{2}^{-1}\end{pmatrix}}.}} The factor in the middle gives another maximal torus in SU(2) obtained by conjugating by J. If a = Σ αiei with |αi| = 1,