Characters of supercuspidal representations ofSL(n)
نویسندگان
چکیده
منابع مشابه
The characters of supercuspidal representations as weighted orbital integrals
Weighted orbital integrals are the terms which occur on the geometric side of the trace formula. We shall investigate these distributions on a p-adic group. We shall evaluate the weighted orbital integral of a supercuspidal matrix coefficient as a multiple of the corresponding character.
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We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation π of a connected reductive p-adic group, subject to the assumption that π is obtained via induction from a representation of an open compact mod centre subgroup. We derive an integral formula for each spherical character belonging to the the basis. This formula involves integration of a part...
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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...
متن کاملConstruction of Tame Supercuspidal Representations
The notion of depth is defined by Moy-Prasad [MP2]. The notion of a generic character will be defined in §9. When G = GLn or G is the multiplicative group of a central division algebra of dimension n with (n, p) = 1, our generic characters are just the generic characters in [My] (where the definition is due to Kutzko). Moreover, in these cases, our construction literally specializes to Howe’s c...
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Let k be a p-adic field of characteristic zero and residue characteristic p. Let G be the group of k-points of a connected reductive group G defined over k. In [38], Yu gives a fairly general construction of supercuspidal representations of G in a certain tame situation. In this paper, subject to some hypotheses on G and k, we prove that all supercuspidal representations arise through his const...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1995
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1995.170.217