Journal of Lie Theory 34 (2024), No. 4, 785--804
Copyright Heldermann Verlag 2024
Duflo's Conjecture for the Restriction of Tempered Representations of GL(n) to a Mirabolic Subgroup
Gang Liu
Institut Elie Cartan de Lorraine, Université de Lorraine, Metz, France
gang.liu@univ-lorraine.fr
Jun Yu
Beijing International Center for Mathematical Research, Peking University, Beijing, P.R. China
junyu@math.pku.edu.cn
We prove Duflo's conjecture in the setting of restriction of tempered representations of GL(n, R) (or GL(n, C)) to a mirabolic subgroup. The proof is mainly based on Sahi's results concerning the branching laws in this setting and precise knowledge of the moment map that we obtain in this paper.
Keywords: Duflo's conjecture, Kirillov's conjecture, orbit method, tempered representations, moment map.
MSC: 22E46.
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