Geodesic
Mackey-Type Identity for Invariant Functions on Lie Algebras of Finite Unitary Groups and an Application
Journal of Lie theory, Tome 33 (2023) no. 1, pp. 149-168
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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 $U(N, \mathbb{F}_{q^2})$.
Classification : 20C33, 22E65, 16T10
Mots-clés : Finite unitary groups, branching graphs, Mackey's theorem 
@article{JLT_2023_33_1_JLT_2023_33_1_a6,
     author = {C. Cuenca and G. Olshanski},
     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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2023_33_1_JLT_2023_33_1_a6/}
}
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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, Tome 33 (2023) no. 1, pp. 149-168. http://geodesic.mathdoc.fr/item/JLT_2023_33_1_JLT_2023_33_1_a6/