Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields

Abstract

Let $F$ be a non-discrete non-Archimedean locally compact field and ${\mathcal{O}}_F$ the ring of integers in $F$. The main results of this paper are Theorem 1.2 that classifies ergodic probability measures on the space $\mathrm{Mat}(\mathbb{N},F)$ of infinite matrices with enties in $F$ with respect to the natural action of the group $\mathrm{GL}(\infty ,{\mathcal{O}}_F)\times \mathrm{GL}(\infty ,{\mathcal{O}}_F)$ and Theorem 1.6 that, for non-dyadic $F$, classifies ergodic probability measures on the space $\mathrm{Sym}(\mathbb{N},F)$ of infinite symmetric matrices with respect to the natural action of the group $\mathrm{GL}(\infty ,{\mathcal{O}}_F)$.

58 pages, all comments are welcome

Cited by in corpus (1)

• Description of unitary representations of the group of infinite $p$-adic integer matrices