Algebraic and Analytic Methods in Representation Theory
Elsevier, Sep 27, 1996 - Mathematics - 343 pages
This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.
Presents several different points of view on key topics in representation theory, from internationally known experts in the field
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Chapter 2 Orbital Varieties Goldie Rank Polynomials and Unitary Highest Weight Modules
Chapter 3 Discontinuous Groups and CliffordKlein Forms of PseudoRiemannian Homogeneous Manifolds
Chapter 4 The Method of Stationary Phase and Applications to Geometry and Analysis on Lie Groups
Chapter 5 The Orbit Method and Unitary Representations for Reductive Lie Groups
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ad(X adjoint action admit a compact algebraic group asymptotic bundle Cartan involution Clifford-Klein form closed subgroup coadjoint orbit coefficients cohomology commutes compact Clifford-Klein form completely prime Corollary critical point decomposition defined Definition denote diffeomorphism differential operators discontinuous group discrete subgroup element elliptic Example formal power series functor G-invariant GL(n group G highest weight modules homogeneous manifold homogeneous spaces homomorphism hyperbolic isomorphic K)-module Lemma Let G Lie algebra linear Math matrix Morse function nilpotent noncompact nondegenerate nonzero orbital varieties oscillatory integrals phase functions polynomials primitive ideal problem Proof properly discontinuous Proposition quotient real reductive group reductive group reductive Lie group reductive type representation of G resp Riemannian Section space of reductive structure subalgebra subgroup of G subspace Suppose G surjective symmetric space T-modules Theorem topology TVG/H unitary representation Weyl group write