On supercuspidal representations of the metaplectic group
نویسندگان
چکیده
منابع مشابه
On the Spectrum of the Metaplectic Group
The subject of this thesis is the theory of nonholomorphic modular forms of non-integral weight, and its applications to arithmetical functions involving Dedekind sums and Kloosterman sums. As was discovered by Andre Weil, automorphic forms of non-integral weight correspond to invariant funtions on Metaplectic groups. We thus give an explicit description of Meptaplectic groups corresponding to ...
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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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where the image of A is in the center of G̃. If G and G̃ are topological groups, and if A is a discrete subgroup of the center of G̃, then we may think of G̃ as a cover of G, in the topological sense. So we will sometimes use the term covering group. Very often for us, A will be the group μn(F ) of n-th roots of unity, in a given field F . We will use this notation only if |μn(F )| = n. By a Metapl...
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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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We recall here the basic definitions needed to construct simple types, with no proofs given of the many claims that we make. For a much more detailed account, see [1] and the many other sources cited therein. Note that most of the statements made here could be proven without much difficulty for the reader who has the time and inclination. Any statements requiring a much more elaborate proof are...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1981
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1981-0610967-7