02857nam 2200553 450 991081176520332120220902081701.00-8218-7602-30-8218-5019-9(CKB)3240000000069541(EBL)3112933(SSID)ssj0000850319(PQKBManifestationID)11515266(PQKBTitleCode)TC0000850319(PQKBWorkID)10832319(PQKB)11270696(MiAaPQ)EBC3112933(RPAM)1389534(PPN)197103340(EXLCZ)99324000000006954119821223h19831983 uy| 0engur|n|---|||||txtccrComplex representations of GL(2,K) for finite fields K /Ilya Piatetski-ShapiroProvidence, Rhode Island :American Mathematical Society,[1983]©19831 online resource (84 p.)Contemporary mathematics,0271-4132 ;16Includes index.Contents -- Introduction -- Chapter 1. Preliminaries: Representation Theory -- the general linear group -- 1. Linear representations of finite groups -- 2. Induced representations -- 3. The Schur algebra -- 4. The group GL(2,K) -- 5. The conjugacy classes of GL(2,K) -- Chapter 2. The representations of GL(2,K) -- 6. The representations of P -- 7. The representations of B -- 8. Inducing characters from B to G -- 9. The Schur algebra of IndGBÎ? -- 10. The dimension of cuspidal representations -- 11. The description of GL(2,K) by generators and relations --12. Non-decomposable characters of Lx --13. Assigning cuspidal representations to non-decomposable characters --14. The correspondence between v and Pv --15. The small Weil group and the small reciprocity law --Chapter 3. г-functions and Bessel functions --16. Whittaker models --17. The г-function of a representation --18. Determination of ρ by гρ --19. The Bessel function of a representation --20. A computation of гρ(ω) for a non-cuspidal ρ --21. A computation of гρ(ω) for a cuspidal ρ --22. The characters of G --References --Index.Contemporary mathematics (American Mathematical Society).160271-4132Linear algebraic groupsRepresentations of groupsFinite fields (Algebra)Linear algebraic groups.Representations of groups.Finite fields (Algebra)512/.2Pi͡atet͡skiĭ-Shapiro I. I(Ilʹi͡a Iosifovich),1929-2009,56905MiAaPQMiAaPQMiAaPQBOOK9910811765203321Complex representations of GL(2,K) for finite fields K380439UNINA