# 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 $\mathrm{GL}(\infty,\mathcal{O}_F)$.
Keywords :
Type de document :
Pré-publication, Document de travail
58 pages, all comments are welcome. 2016
Domaine :

https://hal.archives-ouvertes.fr/hal-01479088
Contributeur : Aigle I2m <>
Soumis le : mardi 28 février 2017 - 16:09:42
Dernière modification le : mercredi 1 mars 2017 - 01:04:41

### Identifiants

• HAL Id : hal-01479088, version 1
• ARXIV : 1605.09600

### Citation

Alexander I. Bufetov, Yanqi Qiu. Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields. 58 pages, all comments are welcome. 2016. <hal-01479088>

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