Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / / George Lusztig.
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-v...
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Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1975 |
Year of Publication: | 2016 |
Language: | English |
Series: | Annals of Mathematics Studies ;
81 |
Online Access: | |
Physical Description: | 1 online resource (104 p.) |
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082 | 0 | 4 | |a 512/.2 |2 23 |
100 | 1 | |a Lusztig, George, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / |c George Lusztig. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2016] | |
264 | 4 | |c ©1975 | |
300 | |a 1 online resource (104 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Annals of Mathematics Studies ; |v 81 | |
505 | 0 | 0 | |t Frontmatter -- |t TABLE OF CONTENTS -- |t INTRODUCTION -- |t CHAPTER 1. PARTIALLY ORDERED SETS AND HOMOLOGY -- |t CHAPTER 2. THE AFFINE STEINBERG MODULE -- |t CHAPTER 3. THE DISTINGUISHED DISCRETE SERIES MODULE -- |t CHAPTER 4. THE CHARACTER OF D(V ) AND THE EIGENVALUE λ (V ) -- |t CHAPTER 5. THE BRAUER LIFTING -- |t INDEX -- |t Backmatter |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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). | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Algebraic fields. | |
650 | 0 | |a Linear algebraic groups. | |
650 | 0 | |a Representations of groups. | |
650 | 0 | |a Series. | |
650 | 7 | |a MATHEMATICS / Group Theory. |2 bisacsh | |
653 | |a Addition. | ||
653 | |a Affine group. | ||
653 | |a Automorphism. | ||
653 | |a Dimension. | ||
653 | |a Eigenvalues and eigenvectors. | ||
653 | |a Endomorphism. | ||
653 | |a Field of fractions. | ||
653 | |a Finite field. | ||
653 | |a Free module. | ||
653 | |a Grothendieck group. | ||
653 | |a Homomorphism. | ||
653 | |a Linear subspace. | ||
653 | |a Morphism. | ||
653 | |a P-adic number. | ||
653 | |a Partially ordered set. | ||
653 | |a Simplicial complex. | ||
653 | |a Tensor product. | ||
653 | |a Theorem. | ||
653 | |a Witt vector. | ||
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Archive 1927-1999 |z 9783110442496 |
776 | 0 | |c print |z 9780691081540 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9781400881765 |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400881765 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400881765/original |
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