Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / George Lusztig.

Format:

Book

Author/Creator:

Lusztig, George, author.

Series:

Annals of mathematics studies ; Number 81.

Annals of Mathematics Studies ; 277

Language:

English

Subjects (All):

Representations of groups.

Linear algebraic groups.

Series.

Algebraic fields.

Physical Description:

1 online resource (107 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes.The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2-1)...(qn-1-1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation △ of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq).

Contents:

Frontmatter

TABLE OF CONTENTS

INTRODUCTION

CHAPTER 1. PARTIALLY ORDERED SETS AND HOMOLOGY

CHAPTER 2. THE AFFINE STEINBERG MODULE

CHAPTER 3. THE DISTINGUISHED DISCRETE SERIES MODULE

CHAPTER 4. THE CHARACTER OF D(V ) AND THE EIGENVALUE λ (V )

CHAPTER 5. THE BRAUER LIFTING

INDEX

Backmatter

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400881765

1400881765

OCLC:

1024047439