Duflo's Conjecture for the Restriction of Tempered Representations of GL(n) to a Mirabolic Subgroup

G. Liu; J. Yu

doi:10.5802/jolt.1361

G. Liu; J. Yu

Journal of Lie Theory, Volume 34 (2024) no. 4, pp. 785-804

Abstract

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.

Zbl

DOI: 10.5802/jolt.1361

Classification: 22E46
Keywords: Duflo's conjecture, Kirillov's conjecture, orbit method, tempered representations, moment map

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     author = {G. Liu and J. Yu},
     title = {Duflo's {Conjecture} for the {Restriction} of {Tempered} {Representations} of {GL(n)} to a {Mirabolic} {Subgroup}},
     journal = {Journal of Lie Theory},
     pages = {785--804},
     year = {2024},
     volume = {34},
     number = {4},
     doi = {10.5802/jolt.1361},
     zbl = {1560.22042},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1361/}
}

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G. Liu; J. 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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