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The Smooth Representations of GL(2,O)

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If you have a question about this talk, please contact Tom Adams.

The representations of p-adic groups are of significant number-theoretic interest. For example, they feature prominently in the p-adic Langlands program and also have connections to the study of automorphic forms. Let K be a p-adic field and O be its ring of integers. To understand the smooth representations of the p-adic group GL(n,K), it is useful to consider the representation theory of its compact subgroups such as GL(n,O). In this talk, after introducing some general p-adic representation theory, I will give an overview of a paper by Alexander Stasinski which classifies the characters of smooth complex representations of GL(2,O). The approach in this paper is based on Clifford theory for finite groups, and a corresponding study of orbits and stabilisers.

This talk is part of the Junior Algebra and Number Theory seminar series.

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