Invariant measures of infinite-dimensional groups over finite fields

Abstract: In this talk, we study the problem of characterizing the set of G-invariant measures on a space of infinite-dimensional matrices over a finite field. The groups G being considered are inductive limits of the finite general linear groups GL(n, q) and the finite even unitary groups $U(2n, q^2)$ over a finite field; our proposed problem is still open in the latter even unitary case and the talk focuses on it. One partial result translates the problem to the classification of positive harmonic functions on branching graphs that are Hall-Littlewood versions of the Young graph. A second partial result is the construction of a large class of invariant measures by means of the Hopf-algebra structure on the ring of symmetric functions. The talk is based on joint work with Grigori Olshanski.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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