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182 MEMORIAL DR, Cambridge, MA 02139

https://math.mit.edu/lg/ #mathematics
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Speaker: Dan Ciubotaru (University of Oxford)

Title: Wavefront sets and unipotent representations of p-adic groups

Abstract: An important invariant for admissible representations of reductive p-adic groups is the wavefront set, the collection of the maximal nilpotent orbits in the support of the orbital integrals that occur in the Harish-Chandra-Howe local character expansion. We compute the geometric and Okada's canonical unramified wavefront sets for representations in Lusztig's category of unipotent reduction for a split group in terms of the Kazhdan-Lusztig parameters. We use this calculation to give a new characterisation of the anti-tempered unipotent Arthur packets. Another interesting consequence is that the geometric wavefront set of a unipotent supercuspidal representation uniquely determines the nilpotent part of the Langlands parameter; this is an extension to p-adic groups of Lusztig's result for unipotent representations of finite groups of Lie type. The talk is based on joint work with Lucas Mason-Brown and Emile Okada.

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