Supercuspidal representations and the theta correspondence
نویسندگان
چکیده
منابع مشابه
Tempered Representations and the Theta Correspondence
Let V be an even dimensional nondegenerate symmetric bilinear space over a nonarchimedean local field F of characteristic zero, and let n be a nonnegative integer. Suppose that σ ∈ Irr(O(V )) and π ∈ Irr(Sp(n, F )) correspond under the theta correspondence. Assuming that σ is tempered, we investigate the problem of determining the Langlands quotient data for π. Let F be a nonarchimedean local f...
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In this paper, we discuss the positivity of the Hermitian form ð; Þp introduced by Li in Invent. Math. 27 (1989) 237–255. Let ðG1;G2Þ be a type I dual pair with G1 the smaller group. Let p be an irreducible unitary representation in the semistable range of yðMG1;MG2Þ (see Communications in Contemporary Mathematics, Vol. 2, 2000, pp. 255–283). We prove that the invariant Hermitian form ð; Þp is ...
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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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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 G be any connected reductive group defined over a nonarchimedean local field F of residual characteristic p. Under some tameness assumptions on G, we construct families of positive-depth supercuspidal representations of G = G(F ). In particular, we classify (§2.7) the representations of G that contain any anisotropic unrefined minimal K-type (in the sense of MoyPrasad [28]) that satisfies a...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1992
ISSN: 0021-8693
DOI: 10.1016/0021-8693(92)90120-b