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

• Autore: Lusztig George
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1975
• Descrizione fisica: 1 online resource (107 pages) : illustrations
• Disciplina: 512/.2
• Soggetto topico: Representations of groups; Linear algebraic groups; Series; Algebraic fields
• Soggetto non controllato: Addition; Affine group; Automorphism; Dimension; Eigenvalues and eigenvectors; Endomorphism; Field of fractions; Finite field; Free module; Grothendieck group; Homomorphism; Linear subspace; Morphism; P-adic number; Partially ordered set; Simplicial complex; Tensor product; Theorem; Witt vector
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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).
• Titolo autorizzato: Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81
• ISBN: 1-4008-8176-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154752503321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 81.