Courses for 2010/2011:
Math 5151 Introduction to Automorphic Representations, Fall semester.
| 課程概述 | Infinite-dimensional
representations of classical groups, GL2. Representations of GL2 over finite fields, local fields. Representations of adelic groups, L-functions. |
| 課程目標 | From representations of groups to Langlands’ program. Start with representations of finite groups, GL2 over finite fields. In the archimedean case, concerns infinite-dimensional of GL2(R) and GL2(C). In the non-archimedean case, supercuspidal representations, principal series representations. The goal is applications of automorphic representations to number theory. |
| 關鍵字 | Group representations, local fields, global fields, GL2. |
| 課程要求 | Complex analysis, basic algebraic number theory, algebra, advanced calculus, basic real analysis. |
| 指定閱讀 | Basic theory of
representations of finite groups. Basic theory of local fields. |
| 參考書目 | D. Bump, Automorphic Forms
and representations, Cambridge U. Press, 1998. C. Bushnell & G. Henniart, Local Langlands conjecture for GL2, Springer, Band 335, Comprehensive studies in Math., 2006. J.-P. Serre, Linear representations of finite groups, Springer GTM Vol 42, 1977. |
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