Representations of p-adic groups via geometric invariant theory

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• Beth Romano (University of Cambridge)
• Tuesday 01 November 2016, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jack Thorne.

Let G be a semisimple split reductive group over a finite extension k of Q_p. Reeder and Yu have given a new construction of supercuspidal representations of G(k) using geometric invariant theory. Their construction is uniform for all p but requires as input stable vectors in certain representations coming from Moy–Prasad filtrations. In joint work, Jessica Fintzen and I have classified the representations of this kind which contain stable vectors; as a corollary, the construction of Reeder-Yu gives new representations when p is small. In my talk, I will give an overview of this work, as well as explicit examples for the case when G = G_2. For these examples, I will explicitly describe the locus of all stable vectors, as well as the Langlands parameters which correspond under the local Langlands correspondence to the representations of G(k).

This talk is part of the Number Theory Seminar series.

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