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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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1975 |
Year of Publication: | 2016 |
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Lusztig, George, author. aut http://id.loc.gov/vocabulary/relators/aut Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / George Lusztig. Princeton, NJ : Princeton University Press, [2016] ©1975 1 online resource (104 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 81 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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). Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Algebraic fields. Linear algebraic groups. Representations of groups. Series. MATHEMATICS / Group Theory. bisacsh 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. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691081540 https://doi.org/10.1515/9781400881765 https://www.degruyter.com/isbn/9781400881765 Cover https://www.degruyter.com/document/cover/isbn/9781400881765/original |
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English |
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Lusztig, George, Lusztig, George, |
spellingShingle |
Lusztig, George, Lusztig, George, Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / Annals of Mathematics Studies ; 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 |
author_facet |
Lusztig, George, Lusztig, George, |
author_variant |
g l gl g l gl |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Lusztig, George, |
title |
Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / |
title_full |
Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / George Lusztig. |
title_fullStr |
Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / George Lusztig. |
title_full_unstemmed |
Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / George Lusztig. |
title_auth |
Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / |
title_alt |
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 |
title_new |
Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / |
title_sort |
discrete series of gln over a finite field. (am-81), volume 81 / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (104 p.) Issued also in print. |
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 |
isbn |
9781400881765 9783110494914 9783110442496 9780691081540 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA171 |
callnumber-sort |
QA 3171 L848 41974EB |
url |
https://doi.org/10.1515/9781400881765 https://www.degruyter.com/isbn/9781400881765 https://www.degruyter.com/document/cover/isbn/9781400881765/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512/.2 |
dewey-sort |
3512 12 |
dewey-raw |
512/.2 |
dewey-search |
512/.2 |
doi_str_mv |
10.1515/9781400881765 |
oclc_num |
979633758 |
work_keys_str_mv |
AT lusztiggeorge discreteseriesofglnoverafinitefieldam81volume81 |
status_str |
n |
ids_txt_mv |
(DE-B1597)468024 (OCoLC)979633758 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 / |
container_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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1770176739919527936 |
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