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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A construction of the supercuspidal representations of $ {\rm GL}\sb n(F),\;F\;p$-adic

Author: Lawrence Corwin
Journal: Trans. Amer. Math. Soc. 337 (1993), 1-58
MSC: Primary 22E50; Secondary 11S37
MathSciNet review: 1079053
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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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Article copyright: © Copyright 1993 American Mathematical Society