A construction of the supercuspidal representations of 𝐺𝐿_{𝑛}(𝐹),𝐹𝑝-adic

Corwin, Lawrence

doi:10.1090/S0002-9947-1993-1079053-7

A construction of the supercuspidal representations of $\textrm {GL}_ n(F),\;F\;p$-adic
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Trans. Amer. Math. Soc. 337 (1993), 1-58 Request permission

Abstract:

Let $F$ be a nondiscrete, locally compact, non-Archimedean field. In this paper, we construct all irreducible supercuspidal representations of $G = {\text {GL}_n}(F)$ For each such representation $\pi$ (which we may as well assume is unitary), we give a subgroup $J$ of $G$ that is compact mod the center $Z$ of $G$ and a (finite-dimensional) representation $\sigma$ of $J$ such that inducing $\sigma$ to $G$ gives $\pi$. The proof that all supercuspidals have been constructed appeals to a theorem (the Matching Theorem) that has been proved by global methods.

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