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Geometric approach to the local Jacquet-Langlands correspondence

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Let F be a p-adic field. The local Jacquet-Langlands correspondence is a natural bijection between irreducible discrete series representations of GLn(F) and irreducible smooth representations of Dx where D is a central division algebra over F. In this talk, under the assumption “inv D = 1/n”, I will explain a geometric approach to construct the bijection. If moreover n is prime, my method provides a purely local proof of the local Jacquet-Langlands correspondence.

This talk is part of the Number Theory Seminar series.

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