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Journal of Lie Theory 32 (2022), No. 2, 519--552
Copyright Heldermann Verlag 2022

A Generalization of Duflo's Conjecture

Hongfeng Zhang
BICMR, Peking University, Beijing, P. R. China

We generalize Duflo's conjecture to understand the branching laws of non-discrete series. We give a unified description on the geometric side about the restriction of an irreducible unitary representation π of GLn(k), k = R or C, to the mirabolic subgroup, where π is attached to a certain kind of coadjoint orbit.

Keywords: Kirillov's conjecture, Duflo's conjecture, orbit method, moment map.

MSC: 22E46, 17B08, 53D20.

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