Analysis on Homogeneous Spaces and Representation Theory of Lie Groups, Okayama-Kyoto
Mathematical Society of Japan, 2000 - Mathematics - 359 pages
This volume is an outgrowth of the activities of the RIMS Research Project, which presented symposia offering both individual lectures on specialized topics and expository courses on current research. The subjects therein reflect very active areas in the representation theory of Lie groups. Also included are various topical interactions with geometry of homogeneous spaces, automorphic forms, quantum groups, special functions, discrete groups, differential equations, and others. Comprising results from active areas of research, this volume should serve as an excellent guide to the representation theory of Lie groups.
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abelian algebraic groups Assume automorphic bijection Borel branching law Cartan subgroup cohomological induction commutative compact Conjecture Corollary corresponding cusp decomposition defined definition denote dimension discrete series representation discretely decomposable eigenvalues element equivalent example exists filtration follows Frobenius splitting functor G-module GL(n group G Harish-Chandra Hence hermitian forms highest weight vector Homogeneous Spaces homomorphism implies infinitesimal character integral invariant involution irreducible unitary representations isomorphic Lemma lemme Let G Lie algebra Lie groups linear Math maximal modular morphism multiplicity non-zero notation Note orbit p-regular parabolic subalgebra parabolic subgroup polynomial principal series principal series representations Proof Proposition proved reductive group representation of G representation theory resp restriction result root satisfying semisimple simple subalgebra subgroup of G submodule subset subspace Suppose symmetric tensor product Theorem tilting modules tout transformation unipotent unique unitary representations Univ Weyl group Whittaker functions Young diagram Zariski dense