# Ergodic measures on infinite skew-symmetric matrices over non-Archimedean local fields

### Yanqi Qiu

Université Paul Sabatier, Toulouse, France

## Abstract

Let $F$ be a non-discrete non-Archimedean locally compact field such that the characteristic char$(F)=2$ and let $O_{F}$ be the ring of integers in $F$. The main results of this paper are Theorem 1.2 that classifies ergodic probability measures on the space Skew$(N,F)$ of infinite skew-symmetric matrices with respect to the natural action of the group GL$(∞,O_{F})$ and Theorem 1.4, that gives an unexpected natural correspondence between the set of GL$(∞,O_{F})$-invariant Borel probability measures on Sym$(N,F)$ and the set of $GL(∞,O_{F})×GL(∞,O_{F})$-invariant Borel probability measures on the space Mat$(N,F)$ of infinite matrices over $F$.

## Cite this article

Yanqi Qiu, Ergodic measures on infinite skew-symmetric matrices over non-Archimedean local fields. Groups Geom. Dyn. 13 (2019), no. 4, pp. 1401–1416

DOI 10.4171/GGD/527