Mackey-Type Identity for Invariant Functions on Lie Algebras of Finite Unitary Groups and an Application

C. Cuenca; G. Olshanski

doi:10.5802/jolt.1278

C. Cuenca; G. Olshanski

Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 149-168

Abstract

The Mackey-type identity mentioned in the title relates the operations of parabolic induction and restriction for invariant functions on the Lie algebras of the finite unitary groups $U(N, \mathbb{F}_{q^2})$. This result is applied to constructing positive harmonic functions on a new branching graph with a negative Hall-Littlewood parameter, as introduced in the authors' previous paper [Advances Math. 395 (2022), 108087]. This in turn implies the existence of an infinite-parameter family of invariant measures for the coadjoint action of an infinite-dimensional analogue of the groups $U(N, \mathbb{F}_{q^2})$.

arXiv Zbl

DOI: 10.5802/jolt.1278

Classification: 20C33, 22E65, 16T10
Keywords: Finite unitary groups, branching graphs, Mackey's theorem

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     title = {Mackey-Type {Identity} for {Invariant} {Functions} on {Lie} {Algebras} of {Finite} {Unitary} {Groups} and an {Application}},
     journal = {Journal of Lie Theory},
     pages = {149--168},
     year = {2023},
     volume = {33},
     number = {1},
     doi = {10.5802/jolt.1278},
     zbl = {1526.22012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1278/}
}

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C. Cuenca; G. Olshanski. Mackey-Type Identity for Invariant Functions on Lie Algebras of Finite Unitary Groups and an Application. Journal of Lie Theory, Volume 33 (2023) no. 1, pp. 149-168. doi: 10.5802/jolt.1278

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