LEADER 02857nam 2200553 450 001 9910811765203321 005 20220902081701.0 010 $a0-8218-7602-3 010 $a0-8218-5019-9 035 $a(CKB)3240000000069541 035 $a(EBL)3112933 035 $a(SSID)ssj0000850319 035 $a(PQKBManifestationID)11515266 035 $a(PQKBTitleCode)TC0000850319 035 $a(PQKBWorkID)10832319 035 $a(PQKB)11270696 035 $a(MiAaPQ)EBC3112933 035 $a(RPAM)1389534 035 $a(PPN)197103340 035 $a(EXLCZ)993240000000069541 100 $a19821223h19831983 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aComplex representations of GL(2,K) for finite fields K /$fIlya Piatetski-Shapiro 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[1983] 210 4$dİ1983 215 $a1 online resource (84 p.) 225 1 $aContemporary mathematics,$x0271-4132 ;$v16 300 $aIncludes index. 327 $aContents -- Introduction -- Chapter 1. Preliminaries: Representation Theory -- the general linear group -- 1. Linear representations of finite groups -- 2. Induced representations -- 3. The Schur algebra -- 4. The group GL(2,K) -- 5. The conjugacy classes of GL(2,K) -- Chapter 2. The representations of GL(2,K) -- 6. The representations of P -- 7. The representations of B -- 8. Inducing characters from B to G -- 9. The Schur algebra of IndGBI?? -- 10. The dimension of cuspidal representations -- 11. The description of GL(2,K) by generators and relations --12. Non-decomposable characters of Lx --13. Assigning cuspidal representations to non-decomposable characters --14. The correspondence between v and Pv --15. The small Weil group and the small reciprocity law --Chapter 3. ?-functions and Bessel functions --16. Whittaker models --17. The ?-function of a representation --18. Determination of ? by ?? --19. The Bessel function of a representation --20. A computation of ??(?) for a non-cuspidal ? --21. A computation of ??(?) for a cuspidal ? --22. The characters of G --References --Index. 410 0$aContemporary mathematics (American Mathematical Society).$v16$x0271-4132 606 $aLinear algebraic groups 606 $aRepresentations of groups 606 $aFinite fields (Algebra) 615 0$aLinear algebraic groups. 615 0$aRepresentations of groups. 615 0$aFinite fields (Algebra) 676 $a512/.2 700 $aPi?atet?skii?-Shapiro$b I. I$g(Il?i?a Iosifovich),$f1929-2009,$056905 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811765203321 996 $aComplex representations of GL(2,K) for finite fields K$9380439 997 $aUNINA