Journal of Lie Theory

no. 4
Duflo's Conjecture for the Restriction of Tempered Representations of GL(n) to a Mirabolic Subgroup
Gang Liu1; Jun Yu2
1Institut Elie Cartan de Lorraine, Université de Lorraine, Metz, France
2Beijing International Center for Mathematical Research, Peking University, Beijing, P.R. China
Journal of Lie Theory, Volume 34 (2024) no. 4, pp. 785-804
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.
DOI: 10.5802/jolt.1361
Classification: 22E46
Keywords: Duflo's conjecture, Kirillov's conjecture, orbit method, tempered representations, moment map

Gang Liu  1 ; Jun Yu  2

1 Institut Elie Cartan de Lorraine, Université de Lorraine, Metz, France
2 Beijing International Center for Mathematical Research, Peking University, Beijing, P.R. China 
Gang Liu; Jun Yu. Duflo's Conjecture for the Restriction of Tempered Representations of GL(n) to a Mirabolic Subgroup. Journal of Lie Theory, Volume 34 (2024) no. 4, pp. 785-804. doi: 10.5802/jolt.1361
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     journal = {Journal of Lie Theory},
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