2016/09/22 by Patrick Delorme, Delorme, P., Pascale Harinck +1
Mathematics · #11F72 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1609.06991
openalex publication_date 2016/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \rm E/\rm F be an unramified quadratic extension of local non archimedean fields of characteristic 0. Let \underlineH be an algebraic reductive group, defined and split over \rm F. We assume that the split connected component of the center of \underlineH is trivial. Let (τ,V) be a \underlineH(\rm F)-distinguished supercuspidal representation of \underlineH(\rm E). Using the recent results of C. Zhang, and the geometric side of a local relative trace formula obtained by P. Delorme, P. Harinck and S. Souaifi, we describe spherical characters associated to \underlineH(\rm F)-invariant linear forms on V in terms of weighted orbital integrals of matrix coefficients of τ.