The nonabelian Fourier transform for elliptic unipotent representations of exceptional p-adic groups

2020/06/24 by Dan Ciubotaru, Ciubotaru, Dan
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2006.13540

openalex publication_date 2020/06/24 · openalex created_date 2020/07/02 · openalex updated_date 2026/07/28

Abstract

We define an involution on the space of elliptic unipotent Langlands parameters of a reductive p-adic group G and verify that when G is split adjoint exceptional, the composition of this involution with the hyperspecial parahoric restriction map agrees with Lusztig's nonabelian Fourier transform for unipotent representations of the finite reductive quotient. This is inspired by recent works of Lusztig on the almost unipotent characters of p-adic groups and of Moeglin and Waldspurger on the elliptic Fourier transform of odd orthogonal groups.

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