Four Drafts of The Representation Theory of the Group of Infinite Matrices over Finite Fields

TL;DR

This paper explores the representation theory of infinite matrix groups over finite fields, including character analysis, limit interpolations, and construction of factor representations, advancing understanding of their algebraic and probabilistic properties.

Contribution

It introduces new methods for analyzing characters and representations of infinite matrix groups over finite fields, bridging finite and infinite group theories.

Findings

Interpolation between inductive and projective limits of finite groups.

Character analysis of almost triangular matrices over finite fields.

A Law of Large Numbers for characters of GL_n(k).

Abstract

Preface (A.Vershik) - about these texts (3.); I.Interpolation between inductive and projective limits of finite groups with applicatons to linear groups over finite fields; II.The characters of the groups of almost triangle matrices over finite filed; III.A Law of Large Numbers for the characters of GL_n(k) over finite field k; IV.An outline of construction of factor representations of the group GLB(F_q).