Unicity of types for supercuspidals

2003/06/06 by Vytautas Paškūnas, Vytautas Paskunas, Paskunas, Vytautas
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.NT #math.RT #msc:22E50

paper · pdf · doi:10.48550/arxiv.math/0306124

42 pages

arxiv created 2003/06/06 · arxiv updated 2009/11/30

Abstract

Let F be a non-Archimedean local field, with the ring of integers \mathfrako_F. Let G=GL_N(F), K=GL_N(\mathfrako_F) and π a supercuspidal representation of G. We show that there exist a unique irreducible smooth representation τ of K, such that the restriction to K of a smooth irreducible representation π' of G contains τ if and only if pi' is isomorphic to π⊗χ∘det, where χ is an unramified quasicharacter of F^×. Moreover, we show that π contains τ with the multiplicity 1. As a corollary we obtain a kind of inertial local Langlands correspondence.

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