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searching for Fixed-point subgroup 11 found (16 total)

Complexification (Lie group) (7,216 words) [view diff] no match in snippet view article

{A={\begin{pmatrix}0&J\\-J&0\end{pmatrix}}.}} Then Sp(n,C) is the fixed point subgroup of the involution θ(g) = A (gt)−1 A−1 of SL(2n,C). It leaves the

System of imprimitivity (3,055 words) [view diff] no match in snippet view article find links to article

on the representation obtained by restricting the cocycle Φ to a fixed point subgroup of the action. We consider this case in the next section. A system

Hermitian symmetric space (7,418 words) [view diff] no match in snippet view article find links to article

semisimple Lie group, σ an automorphism of H of order 2 and Hσ the fixed point subgroup of σ. Let K be a closed subgroup of H lying between Hσ and its identity

Zonal spherical function (6,698 words) [view diff] no match in snippet view article find links to article

Indeed, if τ is the associated period two automorphism of G with fixed point subgroup K, then G = P ⋅ K , {\displaystyle G=P\cdot K,} where P = { g ∈ G

Borel–de Siebenthal theory (3,339 words) [view diff] no match in snippet view article find links to article

semisimple Lie group, σ an automorphism of G of period 2 and Gσ the fixed point subgroup of σ. Let K be a closed subgroup of G lying between Gσ and its identity

Mutation (Jordan algebra) (15,817 words) [view diff] no match in snippet view article

(T_{b})=S_{b^{*}},\,\,\,\theta (W)=(W^{*})^{-1}.}} Let H be the fixed point subgroup of θ in G. Let h {\displaystyle {\mathfrak {h}}} be the fixed point

Kostant's convexity theorem (1,901 words) [view diff] no match in snippet view article find links to article

subgroup fixed by σ and containing the identity component of the fixed point subgroup of σ. Thus G/K is a symmetric space of compact type. Let g {\displaystyle

Plancherel theorem for spherical functions (11,769 words) [view diff] no match in snippet view article find links to article

with σ. The fixed point subgroup of τσ is a compact real form U of G, intersecting G0 in a maximal compact subgroup K0. The fixed point subgroup of τ is K

Invariant convex cone (3,569 words) [view diff] no match in snippet view article find links to article

is a period 2 automorphism σ of the complex symplectic group with fixed point subgroup the real symplectic group. Then x+ = σ(x)^{-1} is an antiautomorphism

Symmetric cone (16,613 words) [view diff] no match in snippet view article find links to article

taking adjoints. Let σg =(g*)−1, period 2 automorphism. Thus K is the fixed point subgroup of σ. Let g {\displaystyle {\mathfrak {g}}} be the Lie algebra of

Oscillator representation (21,532 words) [view diff] no match in snippet view article find links to article

, {\displaystyle M={\begin{pmatrix}0&1\\1&0\end{pmatrix}},} has fixed point subgroup G since σ ( a b c d ) = ( d ¯ c ¯ b ¯ a ¯ ) . {\displaystyle \sigma