Geometry and Representation Theory of Real and p-adic groups / Edition 1

by Juan Tirao, David Vogan, Joe Wolf

Overview

The representation theory of Lie groups plays a central role in both clas­ sical and recent developments in many parts of mathematics and physics. In August, 1995, the Fifth Workshop on Representation Theory of Lie Groups and its Applications took place at the Universidad Nacional de Cordoba in Argentina. Organized by Joseph Wolf, Nolan Wallach, Roberto Miatello, Juan Tirao, and Jorge Vargas, the workshop offered expository courses on current research, and individual lectures on more specialized topics. The present vol­ ume reflects the dual character of the workshop. Many of the articles will be accessible to graduate students and others entering the field. Here is a rough outline of the mathematical content. (The editors beg the indulgence of the readers for any lapses in this preface in the high standards of historical and mathematical accuracy that were imposed on the authors of the articles. ) Connections between flag varieties and representation theory for real re­ ductive groups have been studied for almost fifty years, from the work of Gelfand and Naimark on principal series representations to that of Beilinson and Bernstein on localization. The article of Wolf provides a detailed introduction to the analytic side of these developments. He describes the construction of standard tempered representations in terms of square-integrable partially harmonic forms (on certain real group orbits on a flag variety), and outlines the ingredients in the Plancherel formula. Finally, he describes recent work on the complex geometry of real group orbits on partial flag varieties.

Product Details

ISBN-13:	9780817639310
Publisher:	Birkhäuser Boston
Publication date:	11/18/1997
Series:	Progress in Mathematics , #158
Edition description:	1998
Pages:	326
Product dimensions:	6.10(w) x 9.25(h) x 0.35(d)

Table of Contents

The Spherical Dual for p-adic Groups.- Finite Rank Homogeneous Holomorphic Bundles in Flag Spaces.- Etale Affine Representations of Lie Groups.- Compatibility between a Geometric Character Formula and the Induced Character Formula.- An Action of the R-Group on the Langlands Subrepresentations.- Geometric Quantization for Nilpotent Coadjoint Orbits.- A Remark on Casselman’s Comparison Theorem.- Principal Covariants, Multiplicity-Free Actions, and the K-Types of Holomorphic Discrete Series.- Whittaker Models for Carayol Representations of GLN(F).- Smooth Representations of Reductive p-adic Groups: An Introduction to the theory of types.- Regular Metabelian Lie Algebras.- Equivariant Derived Categories, Zuckerman Functors and Localization.- A Comparison of Geometric Theta Functions for Forms of Orthogonal Groups.- Flag Manifolds and Representation Theory.

Editorial Reviews

Presents 14 papers on current research and some specialized topics from an August 1995 workshop in Cordoba, Argentina. Many should be accessible to graduate students and other newcomers to the representation theory of Lie groups. Among the topics are the spherical dual, finite rank homogeneous holomorphic bundles in flag spaces, geometric quantization for nilpotent coadjoint orbits, a remark of Casselman's comparison theorem, regular metabelian Lie algebras, and a comparison of geometric theta functions for forms of orthogonal groups. No index. Annotation c. by Book News, Inc., Portland, Or.

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