
Journal of Lie Theory 33 (2023), No. 1, 149168 Copyright Heldermann Verlag 2023 MackeyType Identity for Invariant Functions on Lie Algebras of Finite Unitary Groups and an Application Cesar Cuenca Department of Mathematics, Harvard University, Cambridge, U.S.A. cesar.a.cuenk@gmail.com Grigori Olshanski (1) Institute for Information Transmission Problems, Moscow, Russia (2) Skolkovo Institute of Science and Technology, Moscow, Russia (3) Faculty of Mathematics, HSE University, Moscow, Russia olsh2007@gmail.com [Abstractpdf] The Mackeytype 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 HallLittlewood parameter, as introduced in the authors' previous paper [Advances Math. 395 (2022), 108087]. This in turn implies the existence of an infiniteparameter family of invariant measures for the coadjoint action of an infinitedimensional analogue of the groups $U(N, \mathbb{F}_{q^2})$. Keywords: Finite unitary groups, branching graphs, Mackey's theorem. MSC: 20C33, 22E65, 16T10. [ Fulltextpdf (192 KB)] for subscribers only. 