# Infinite-dimensional groups over finite fields and Hall-Littlewood symmetric functions

@article{Cuenca2021InfinitedimensionalGO,
title={Infinite-dimensional groups over finite fields and Hall-Littlewood symmetric functions},
author={Cesar Cuenca and Grigori Olshanski},
year={2021}
}
• Published 3 February 2021
• Mathematics
3 Citations
• Mathematics
• 2022
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, F q 2 ).
We prove that the boundary of the Hall-Littlewood t -deformation of the Gelfand-Tsetlin graph is parametrized by inﬁnite integer signatures, extending results of Gorin [Gor12] and Cuenca [Cue18] on
. We introduce and study multiple partition structures which are sequences of probability measures on families of Young diagrams subjected to a consistency condition. The multiple partition

## References

SHOWING 1-10 OF 35 REFERENCES

• Mathematics
• 2007
The history of these drafts is described in the preface written by the first author; the drafts were written in 1997–2000, when the authors studied asymptotic representation theory. Each draft is
We show that every countable direct system of finite-dimensional real or complex Lie groups has a direct limit in the category of Lie groups modelled on locally convex spaces. This enables us to push
• Mathematics
Asymptotic representation theory of general linear groups $$\hbox {GL}(n,F_\mathfrak {q})$$GL(n,Fq) over a finite field leads to studying probability measures $$\rho$$ρ on the group $$\mathbb {U}$$U