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Number theoretic applications of the theory of types for p-adic groups

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Let G be a reductive group over a nonarchimedean local field. A type for G is a representation of a compact open subgroup K that characterizes representations of G up to inertia. A variation on this theme is to fix K to be a maximal compact subgroup. I will describe a partial classification of such types for G = GL(n), which yields an inertial local Langlands correspondence. I will also define a notion of global type, and give some applications to automorphic forms and Galois representations.

This talk is part of the Number Theory Seminar series.

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