Character rigidity for special linear groups

TL;DR

This paper investigates characters on special linear groups over various rings, providing applications to measure-preserving actions, superrigidity, and almost homomorphisms, advancing understanding of their algebraic and analytical properties.

Contribution

It introduces new results on characters of SL_n(R) over infinite fields and localizations, with applications to superrigidity and measure-preserving actions.

Findings

Characters on SL_n(R) are classified for certain rings.

Applications to measure-preserving actions demonstrate rigidity phenomena.

Results contribute to understanding of operator-algebraic superrigidity.

Abstract

In this paper we study characters on special linear groups SL_n(R), where R is either an infinite field or the localization of an order in a number field. We give several applications to the theory of measure preserving actions, operator-algebraic superrigidity, and almost homomorphisms.