Singular Unitary Representations and Discrete Series for Indefinite Stiefel Manifolds U (Memoirs of the American Mathematical Society) - Softcover

Kobayashi, Toshiyuki

Softcover

ISBN 10: 0821825240 ISBN 13: 9780821825242

Publisher: Amer Mathematical Society, 1992

Synopsis

Interesting classes of (g, K)-modules are often described naturally in terms of cohomologically induced representations in various settings, such as unitary highest weight modules, the theory of dual reductive pairs, discrete series for semisimple theory of dual reductive pairs, discrete series for semisimple symmetric spaces, etc. These have been stimulating the study of algebraic properties of derived functor modules. Now an almost satisfactory theory on derived functor modules, including a functorial property about unitarizability, has been developed in the good range of parameters, though some subtle problems still remain. This work treats a relatively singular part of the unitary dual of pseudo-orthogonal groups U(p, q;F) over F = R, C and H. These representations arise from discrete series for indefinite Stiefel manifolds U(p, q;F)/U(p - m, q, F)(2m 4p). Thanks to the duality theorem between d-module construction and Zuckerman's derived functor modules (ZDF-modules), these discrete series are naturally described in terms of ZF-modules with possibly singular parameters. The author's approach is algebraic and covers some parameters wandering outside the canonical Weyl cha

About this edition

• Publisher: Amer Mathematical Society
• Publication date: 1992
• ISBN 10: 0821825240
• ISBN 13: 9780821825242
• Binding: Paperback
• Number of pages: 106