Self-dual representations with vectors fixed under an Iwahori subgroup

2012/09/13 by Kumar Balasubramanian, Balasubramanian, Kumar
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1209.2798

arxiv created 2012/09/22 · arxiv updated 2012/09/25

Abstract

Let G be the group of F-points of a split connected reductive F-group over a non-Archimedean local field F of characteristic 0. Let π be an irreducible smooth self-dual representation of G. The space W of π carries a non-degenerate G-invariant bilinear form ( , ) which is unique up to scaling. The form is easily seen to be symmetric or skew-symmetric and we set ε(π)=± 1 accordingly. In this article, we show that ε(π)=1 when π is a generic representation of G with non-zero vectors fixed under an Iwahori subgroup I.

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