Effective and Infinite-Rank Superrigidity in the Context of Representation Stability

Abstract

We discuss certain effective improvements on superrigidity for $S{L}_n(\mathbb{Z})$ for finite $n>2$. Using these ideas we then use superrigidity to prove a representation stability theorem about pointwise finite dimensional $VIC(\mathbb{Z})$-modules, which itself can be viewed as a superrigidity theorem for $VIC(\mathbb{Z})$ and $G{L}_{\infty }(\mathbb{Z})$

40 pages