03988nam 22008415 450 991015475250332120190708092533.01-4008-8176-510.1515/9781400881765(CKB)3710000000620145(SSID)ssj0001651264(PQKBManifestationID)16426235(PQKBTitleCode)TC0001651264(PQKBWorkID)13011947(PQKB)11054564(MiAaPQ)EBC4738575(DE-B1597)468024(OCoLC)1024047439(OCoLC)979633758(DE-B1597)9781400881765(EXLCZ)99371000000062014520190708d2016 fg engurcnu||||||||txtccrDiscrete Series of GLn Over a Finite Field. (AM-81), Volume 81 /George LusztigPrinceton, NJ : Princeton University Press, [2016]©19751 online resource (107 pages) illustrationsAnnals of Mathematics Studies ;277Bibliographic Level Mode of Issuance: Monograph0-691-08154-9 Includes bibliographical references and index.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 -- BackmatterIn 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).Annals of mathematics studies ;Number 81.Representations of groupsLinear algebraic groupsSeriesAlgebraic fieldsAddition.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.Representations of groups.Linear algebraic groups.Series.Algebraic fields.512/.2Lusztig George, 59231DE-B1597DE-B1597BOOK9910154752503321Discrete Series of GLn Over a Finite Field. (AM-81), Volume 812788687UNINA