Mark Reeder

Abstract: The local Langlands conjecture predicts that irreducible square-integrable representations of a reductive group G over a p-adic field k should be (roughly) parametrized by certain finite solvable subgroups of a complex Lie group LG which is in some sense dual to G. I will discuss a uniform family of examples of the local Langlands conjecture, which is very simple, yet seems to have gone unnoticed until now. These examples indicate a strong interaction between a local Galois group and the structure of complex Lie groups, and that this interaction is governed by the L² representations of p-adic groups. This is joint work with Benedict Gross.

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