Representations of Compact Lie Groups |
Contents
CHAPTER I | 1 |
The Exponential | 24 |
Homogeneous Spaces and Quotient Groups | 30 |
Copyright | |
36 other sections not shown
Common terms and phrases
abelian adjoint representation automorphism basis bijection called canonical Cartan subgroup Clifford algebra closed subgroup coefficients compact connected Lie compact Lie group complex compute conjugation connected Lie group contained corresponding defined Definition denote det(w diffeomorphism differentiable direct sum dominant weight e₁ element exponential map finite finite-dimensional follows G-module given GL(n hence homomorphism induces injective inner product integral forms invariant inverse roots Irr(G irreducible characters irreducible representations isomorphism left-invariant Lemma Let G Lie algebra Lie group G linear LT(n manifold matrix maximal torus module morphism multiplication operates orthogonal polynomial positive roots PROOF Proposition quaternionic representation of G representation ring root system self-conjugate semisimple Show SO(n Sp(n Spin(2n Spin(m structure SU(n submodules subspace summands surjective symmetric theorem topology trivial U₁ V₁ vector space W-invariant Weyl chamber Weyl group