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

Couverture
Princeton University Press, 2 mars 2016 - 104 pages

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).

 

Pages sélectionnées

Table des matières

INTRODUCTION
3
CHAPTER 1 Partially Ordered Sets and Homology
5
CHAPTER 2 The Affine Steinberg Module
30
CHAPTER 3 The Distinguished Discrete Series Module
43
CHAPTER 4 The Character of DV and the Eigenvalue AV
66
CHAPTER 5 The Brauer Lifting
80
INDEX
99
Droits d'auteur

Autres éditions - Tout afficher

The Discrete Series of GLn Over a Finite Field
George Lusztig
Aperçu limité - 1974
The Discrete Series of GLn Over a Finite Field
George Lusztig
Aperçu limité - 1974
The Scottish Educational Journal, Volume 34,Numéro 2

Affichage d'extraits - 1951
Tout afficher »

Expressions et termes fréquents

A-modules acts affine space affine subspaces anisotropic Applying associate Assume br(V canonical character clear clearly coefficient system commutative complete complete flags Consider consisting contain COROLLARY correspondence covering cycle condition define definition denote described determined discrete series easy elements equal exact sequence exists F-vector fact field finite field fixed flag follows formula function given gives GL(V GL(V)-module hence homology homomorphism i-dimensional identity independent induction integer invariant irreducible isomorphism isotypic leaves lemma linear subspaces maximal module Moreover natural Note observe obvious permutation precisely Proof proposition prove regarded Remark representation restriction result ring Rw G satisfies shows simplicial complex space of dimension subgroup subset supp Theorem unique values vanishes vector space weight write zero

Informations bibliographiques

TitreDiscrete Series of GLn Over a Finite Field. (AM-81), Volume 81
Volume 81 de Annals of Mathematics Studies
AuteurGeorge Lusztig
ÉditeurPrinceton University Press, 2016
ISBN1400881765, 9781400881765
Longueur104 pages
  
Exporter la citationBiBTeX EndNote RefMan