Representations with Iwahori-fixed vectors
نویسنده
چکیده
• Generic algebras • Strict Iwahori-Hecke algebras • Representations with Iwahori-fixed vectors • Proof of the Borel-Matsumoto theorem • Irreducibility criteria Using the ideas of [Casselman 1980] descended from the Borel-Matsumoto theorem on admissible representations of p-adic reductive groups containing Iwahori-fixed vectors, it is possible to give an easily verifiable sufficient criterion for irreducibility of degenerate principal series. This result is not comparable to irreducibility results such as [Muić-Shahidi 1998], but is easily proven and easily applied. Let G be a p-adic reductive group, P a minimal parabolic, N its unipotent radical, B the Iwahori subgroup matching P , and K a maximal compact subgroup containing B. As usual, a character χ : P/N → C× is unramified if it is trivial on P ∩K. Let δ = δP be the modular function on P , and ρ = ρP = δ P the square root of this modular function.
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