On cuspidal representations of $p$-adic reductive groups
نویسندگان
چکیده
منابع مشابه
EXISTENCE OF CUSPIDAL REPRESENTATIONS OF p-ADIC REDUCTIVE GROUPS
We prove that any reductive group G over a non-Archimedean local field has a cuspidal complex representation.
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Smooth representations of p-adic groups arise in number theory mainly through the study of automorphic representations, and thus in the end, for example, from modular forms. We saw in the first lecture by Matt Emerton that a modular form, thought of as function on the set of lattices with level N structure, we obtain a function in C(GL2(Z)\GL2(R) × GL2(Z/N),C) satisfying certain differential eq...
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Cuspidal representations of a reductive p-adic group G over a field of characteristic different from p are relatively injective and projective with respect to extensions that split by a U-equivariant linear map for any subgroup U that is compact modulo the centre. The category of smooth representations over a field whose characteristic does not divide the pro-order of G is the product of the su...
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Let F be a non-Archimedean locally compact field, let G be a split connected reductive group over F . For a parabolic subgroup Q ⊂ G and a ring L we consider the G-representation on the L-module (∗) C∞(G/Q, L)/ ∑
متن کاملSUPERCUSPIDAL CHARACTERS OF REDUCTIVE p-ADIC GROUPS
We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu’s construction from data satisfying a certain compactness condition. Each character is expressed in terms of a depth-zero character of a smaller group, the (linear) characters appearing in Yu’s construction, Fourier transforms of orbital integr...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1975
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1975-13861-4