LEADER 03988nam 22008415 450 001 9910154752503321 005 20190708092533.0 010 $a1-4008-8176-5 024 7 $a10.1515/9781400881765 035 $a(CKB)3710000000620145 035 $a(SSID)ssj0001651264 035 $a(PQKBManifestationID)16426235 035 $a(PQKBTitleCode)TC0001651264 035 $a(PQKBWorkID)13011947 035 $a(PQKB)11054564 035 $a(MiAaPQ)EBC4738575 035 $a(DE-B1597)468024 035 $a(OCoLC)1024047439 035 $a(OCoLC)979633758 035 $a(DE-B1597)9781400881765 035 $a(EXLCZ)993710000000620145 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDiscrete Series of GLn Over a Finite Field. (AM-81), Volume 81 /$fGeorge Lusztig 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$dİ1975 215 $a1 online resource (107 pages) $cillustrations 225 0 $aAnnals of Mathematics Studies ;$v277 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-691-08154-9 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tTABLE OF CONTENTS -- $tINTRODUCTION -- $tCHAPTER 1. PARTIALLY ORDERED SETS AND HOMOLOGY -- $tCHAPTER 2. THE AFFINE STEINBERG MODULE -- $tCHAPTER 3. THE DISTINGUISHED DISCRETE SERIES MODULE -- $tCHAPTER 4. THE CHARACTER OF D(V ) AND THE EIGENVALUE ? (V ) -- $tCHAPTER 5. THE BRAUER LIFTING -- $tINDEX -- $tBackmatter 330 $aIn this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes.The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2-1)...(qn-1-1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation ? of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq). 410 0$aAnnals of mathematics studies ;$vNumber 81. 606 $aRepresentations of groups 606 $aLinear algebraic groups 606 $aSeries 606 $aAlgebraic fields 610 $aAddition. 610 $aAffine group. 610 $aAutomorphism. 610 $aDimension. 610 $aEigenvalues and eigenvectors. 610 $aEndomorphism. 610 $aField of fractions. 610 $aFinite field. 610 $aFree module. 610 $aGrothendieck group. 610 $aHomomorphism. 610 $aLinear subspace. 610 $aMorphism. 610 $aP-adic number. 610 $aPartially ordered set. 610 $aSimplicial complex. 610 $aTensor product. 610 $aTheorem. 610 $aWitt vector. 615 0$aRepresentations of groups. 615 0$aLinear algebraic groups. 615 0$aSeries. 615 0$aAlgebraic fields. 676 $a512/.2 700 $aLusztig$b George, $059231 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154752503321 996 $aDiscrete Series of GLn Over a Finite Field. (AM-81), Volume 81$92788687 997 $aUNINA