Complex representations of GL(2,K) for finite fields K / / Ilya Piatetski-Shapiro

• Record Nr.: UNINA9910788780003321
• Autore: Pi͡atet͡skiĭ-Shapiro I. I (Ilʹi͡a Iosifovich), <1929-2009, >
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [1983]; ©1983
• ISBN: 0-8218-7602-3; 0-8218-5019-9
• Descrizione fisica: 1 online resource (84 p.)
• Collana: Contemporary mathematics, , 0271-4132 ; ; 16
• Disciplina: 512/.2
• Soggetti: Linear algebraic groups; Representations of groups; Finite fields (Algebra)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Includes index.
• Nota di contenuto: 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.