Geometry and representation theory of real and p-adic groups

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Geometry and representation theory of real and p-adic groups

Juan Tirao, David A. Vogan, Jr., Joseph A. Wolf, editors

（Progress in mathematics, vol. 158）

Birkhäuser, c1998

  • : us
  • : gw

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Note

Papers from the Fifth Workshop on Representation Theory of Lie Groups and Its Applications, held Aug. 1995 at the Universidad Nacional de Córdoba in Argentina

Includes bibliographical references

Description and Table of Contents

Volume

: us ISBN 9780817639310

Description

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 introduc tion 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.

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.
Volume

: gw ISBN 9783764339319

Description

This text provides a thorough introduction to the more active parts of representation theory and to some of its ongoing applications.

Table of Contents

  • The spherical dual for $p$-adic groups, Dan Barbasch
  • finite rank homogeneous holomorphic bundles in flag spaces, Tim Bratten
  • etale affine representations of lie groups, Dietrich Burde
  • compatibility between a geometric character formula and the induced character formula, Esther Galina
  • an action of the R-group on the Langlands subrepresentations, Eugenio Garnica Vigil
  • geometric quantization for nilpotent coadjoint orbits, William Graham and David A. Vogan Jr
  • a remark on Casselman's comparison theorem, Henryk Hecht and Joseph L. Taylor
  • principal covariants, multiplicity-free actions and the $k$-types of holomorphic discrete series, Roger Howe and Hanspeter Kraft.

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