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Longer titles found: Parabolic subgroup of a reflection group (view), Siegel parabolic subgroup (view)

searching for Parabolic subgroup 40 found (58 total)

Generalized flag variety (2,475 words) [view diff] exact match in snippet view article find links to article

X has an F-rational point, then it is isomorphic to G/P for some parabolic subgroup P of G. A projective homogeneous variety may also be realised as the

Parabolic induction (389 words) [view diff] exact match in snippet view article find links to article

= M A N {\displaystyle P=MAN} is the Langlands decomposition of a parabolic subgroup P, then parabolic induction consists of taking a representation of

Langlands decomposition (136 words) [view diff] exact match in snippet view article find links to article

In mathematics, the Langlands decomposition writes a parabolic subgroup P of a semisimple Lie group as a product P = M A N {\displaystyle P=MAN} of a reductive

Harish-Chandra transform (142 words) [view diff] exact match in snippet view article find links to article

linear map from functions on a reductive Lie group to functions on a parabolic subgroup. It was introduced by Harish-Chandra (1958, p.595). The Harish-Chandra

Parabolic geometry (differential geometry) (435 words) [view diff] exact match in snippet view article

space G/P which is the quotient of a semisimple Lie group G by a parabolic subgroup P. More generally, the curved analogs of a parabolic geometry in this

Schubert variety (946 words) [view diff] exact match in snippet view article find links to article

{\displaystyle G} with a Borel subgroup B {\displaystyle B} and a standard parabolic subgroup P {\displaystyle P} , it is known that the homogeneous space G / P

Homogeneous variety (52 words) [view diff] exact match in snippet view article find links to article

algebraic variety of the form G/P, G a linear algebraic group, P a parabolic subgroup. It is a smooth projective variety. If P is a Borel subgroup, it is

Mirabolic group (342 words) [view diff] exact match in snippet view article find links to article

a mirabolic subgroup in the projective general linear group is a parabolic subgroup consisting of all elements fixing a given point of projective space

Cusp form (657 words) [view diff] exact match in snippet view article find links to article

representations. Consider P = M U {\displaystyle P=MU} a standard parabolic subgroup of some reductive group G {\displaystyle G} (over A {\displaystyle

Iwahori subgroup (800 words) [view diff] exact match in snippet view article find links to article

union of double cosets of an Iwahori subgroup, so is analogous to a parabolic subgroup of an algebraic group. Iwahori subgroups are named after Nagayoshi

Roger Wolcott Richardson (332 words) [view diff] exact match in snippet view article find links to article

until his death. Richardson's best known result states that if P is a parabolic subgroup of a reductive group, then P has a dense orbit on its nilradical,

(B, N) pair (986 words) [view diff] exact match in snippet view article

group G=G(K) has a BN pair in which B=P(K), where P is a minimal parabolic subgroup of G, and N=N(K), where N is the normalizer of a split maximal torus

Representation theory of SL2(R) (1,827 words) [view diff] exact match in snippet view article

case of the group SL(2, R), there is up to conjugacy only one proper parabolic subgroup, the Borel subgroup of the upper-triangular matrices of determinant

Standard monomial theory (982 words) [view diff] exact match in snippet view article find links to article

monomial theory, to extend Hodge's work to varieties G/P, for P any parabolic subgroup of any reductive algebraic group in any characteristic, by giving

Stable principal bundle (1,338 words) [view diff] exact match in snippet view article find links to article

\sigma :U\to P/Q} for Q ⊂ G {\displaystyle Q\subset G} a maximal parabolic subgroup where U ⊂ X {\displaystyle U\subset X} is some open subset with the

Jacquet module (369 words) [view diff] exact match in snippet view article find links to article

algebraic group G over a local field, and N is the unipotent radical of a parabolic subgroup of G. In the case of p-adic groups, they were studied by Hervé Jacquet (1971)

Reductive group (7,845 words) [view diff] exact match in snippet view article find links to article

diagram). Let r be the order of Δ, the semisimple rank of G. Every parabolic subgroup of G is conjugate to a subgroup containing B by some element of G(k)

Lie group decomposition (346 words) [view diff] exact match in snippet view article find links to article

orthogonalization). The Langlands decomposition P = MAN writes a parabolic subgroup P of a Lie group as the product of semisimple, abelian, and nilpotent

Hilbert's fifteenth problem (971 words) [view diff] exact match in snippet view article find links to article

ring H*(G/P) of a flag manifold G/P, where G is a Lie group and P a parabolic subgroup of G. The additive structure of the ring H*(G/P) is given by the basis

Furstenberg boundary (558 words) [view diff] exact match in snippet view article find links to article

these are homogeneous spaces of G that are quotients of G by some parabolic subgroup, which can be described completely in terms of root data and a given

Eisenstein integral (470 words) [view diff] exact match in snippet view article find links to article

where: x is an element of a semisimple group G P = MAN is a cuspidal parabolic subgroup of G ν is an element of the complexification of a a is the Lie algebra

Alvis–Curtis duality (518 words) [view diff] exact match in snippet view article find links to article

Coxeter system of G. The character ζ PJ is the truncation of ζ to the parabolic subgroup PJ of the subset J, given by restricting ζ to PJ and then taking the

Prehomogeneous vector space (1,712 words) [view diff] exact match in snippet view article find links to article

1974, Richardson observed that if H is a semisimple Lie group with a parabolic subgroup P, then the action of P on the nilradical p {\displaystyle {\mathfrak

Langlands classification (607 words) [view diff] exact match in snippet view article find links to article

parameterized by triples (F, σ, λ) where F is a subset of Δ Q is the standard parabolic subgroup of F, with Langlands decomposition Q = MAN σ is an irreducible tempered

Hermitian symmetric space (7,418 words) [view diff] exact match in snippet view article find links to article

connected. It follows that H / K is simply connected and there is a parabolic subgroup P in the complexification G of H such that H / K = G / P. In particular

Flag (linear algebra) (897 words) [view diff] exact match in snippet view article

general linear group), and the stabilizer of any partial flags is a parabolic subgroup. The stabilizer subgroup of a flag acts simply transitively on adapted

Tempered representation (1,430 words) [view diff] exact match in snippet view article find links to article

representations. If P=MAN is the Langlands decomposition of a cuspidal parabolic subgroup, then a basic representation is defined to be the parabolically induced

Steinberg representation (895 words) [view diff] exact match in snippet view article find links to article

the representation induced from the identity representation of the parabolic subgroup. The Steinberg representation is both regular and unipotent, and is

Invariant differential operator (1,324 words) [view diff] exact match in snippet view article find links to article

homogeneous parabolic geometries, i.e. when G is semi-simple and H is a parabolic subgroup, are given dually by homomorphisms of generalized Verma modules. Given

Period mapping (2,076 words) [view diff] exact match in snippet view article find links to article

in B as above. The flag variety is a quotient of a Lie group by a parabolic subgroup, and the monodromy group is an arithmetic subgroup of the Lie group

Co-Hopfian group (1,533 words) [view diff] exact match in snippet view article find links to article

parabolic for some k >1 or G splits over a virtually cyclic or a parabolic subgroup. Grigorchuk group G of intermediate growth is not co-Hopfian. Thompson

Glossary of Lie groups and Lie algebras (3,110 words) [view diff] exact match in snippet view article find links to article

see #compact. 2. For "maximal torus", see #torus. parabolic 1. Parabolic subgroup 2. Parabolic subalgebra. positive For "positive root", see #positive

Building (mathematics) (3,170 words) [view diff] exact match in snippet view article

of B a Borel subgroup and any group containing a Borel subgroup a parabolic subgroup, the vertices of the building X correspond to maximal parabolic subgroups;

Convexity (algebraic geometry) (1,389 words) [view diff] exact match in snippet view article

homogenous spaces G / P {\displaystyle G/P} where P {\displaystyle P} is a parabolic subgroup of G {\displaystyle G} . These have globally generated sections since

Arthur–Selberg trace formula (2,203 words) [view diff] exact match in snippet view article find links to article

_{n\in N(A)}f(xny)\,dn=0} for any unipotent radical N of a proper parabolic subgroup (defined over F) and any x, y in G(A), then the operator R(f) has

Torsor (algebraic geometry) (2,638 words) [view diff] exact match in snippet view article

{Spec} \mathbf {F} _{q}} is trivial. (Lang's theorem.) If P is a parabolic subgroup of a smooth affine group scheme G with connected fibers, then its

Complex affine space (2,538 words) [view diff] exact match in snippet view article find links to article

C) acts on P(A). The stabilizer of the hyperplane at infinity is a parabolic subgroup, which is the automorphism group of A. It is isomorphic (but not naturally

Borel–de Siebenthal theory (3,339 words) [view diff] exact match in snippet view article find links to article

torus S. It follows that G / K is simply connected and there is a parabolic subgroup P in the complexification GC of G such that G / K = GC / P. In particular

Grassmannian (8,384 words) [view diff] exact match in snippet view article find links to article

as an algebraic variety. In particular, H {\displaystyle H} is a parabolic subgroup of G L ( V ) {\displaystyle \mathrm {GL} (V)} . Over R {\displaystyle

Complexification (Lie group) (7,216 words) [view diff] exact match in snippet view article

Helgason (1994), Duistermaat & Kolk (2000) and Sepanski (2007). The parabolic subgroup P can also be written as a union of double cosets of B P = ⋃ σ ∈ W