Complex Representations of GL (2,K) for Finite Fields K.

Intro -- 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 IndGBμ -- 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.