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Record Nr. |
UNINA9910154752503321 |
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Autore |
Lusztig George |
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Titolo |
Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / / George Lusztig |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©1975 |
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ISBN |
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Descrizione fisica |
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1 online resource (107 pages) : illustrations |
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Collana |
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Annals of Mathematics Studies ; ; 277 |
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Disciplina |
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Soggetti |
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Representations of groups |
Linear algebraic groups |
Series |
Algebraic fields |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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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 |
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