Algebraic and Analytic Methods in Representation Theory
Academic Press, 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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A G X(T action of G ad(X adjoint action admit a compact algebraic group bundle Cartan decomposition Cartan involution closed subgroup coadjoint orbit cohomology commutes compact Clifford—Klein form completely prime complex Corollary critical point decomposition deﬁned denote diffeomorphism differential operators discontinuous group discrete subgroup Dixmier algebra element elliptic Example ﬁnd ﬁrst formal power series functor G-invariant group G highest weight modules homogeneous manifold homogeneous spaces homomorphism hyperbolic identiﬁed inﬁnite invariant isomorphic Lemma Lie algebra linear Math matrix Morse function nilpotent noncompact nondegenerate orbital varieties oscillatory integrals phase functions polynomials primitive ideals problem Proof properly discontinuous Proposition quotient real reductive group reductive group reductive Lie group reductive type representation of G representation theory resp result Riemannian satisﬁed Section semisimple Lie space of reductive structure subalgebra subgroup of G subspace Suppose G surjective symmetric space Theorem topology unitary representation Weyl group write