Construction of Tame Supercuspidal Representations
نویسنده
چکیده
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 construction as formulated in [My], and it is known that the construction yields all supercuspidal representations ([My], [HM]). Notice that the initial datum in our construction consists of very simple objects: linear characters and supercuspidal representations of depth zero. The latter are well understood by the work of Moy, Prasad, and Morris (see §3). By the work of Howe, irreducible supercuspidal representations of GLn(F ) with (n, p) = 1 are parametrized by certain characters of E∗ as E varies through
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