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

  title={Infinite-dimensional groups over finite fields and Hall-Littlewood symmetric functions},
  author={Cesar Cuenca and Grigori Olshanski},
  journal={Advances in Mathematics},

Mackey-type identity for invariant functions on Lie algebras of finite unitary groups and an application

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 ).

Hall-Littlewood polynomials, boundaries, and $p$-adic random matrices

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

Multiple Partition Structures and Harmonic Functions on Branching Graphs

. 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



On the characteristic map of finite unitary groups

Four drafts on the representation theory of the group of infinite matrices over a finite field

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

Fundamentals of direct limit Lie theory

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

Hermitian Varieties in a Finite Projective Space PG(N, q 2)

The geometry of quadric varieties (hypersurfaces) in finite projective spaces of N dimensions has been studied by Primrose (12) and Ray-Chaudhuri (13). In this paper we study the geometry of another

Fourier transforms, nilpotent orbits, Hall polynomials and Green functions

Let G be a connected reductive group defined over the finite field 픽 q , and let Open image in new window be its Lie algebra. Let F: G → G be the corresponding Frobenius endomorphism and write also

Law of Large Numbers for infinite random matrices over a finite field

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

Conjugacy classes in linear groups