Hua measures on the space of $p$-adic matrices and inverse limits of Grassmannians

TL;DR

This paper develops $p$-adic analogs of Hua measures on inverse limits of Grassmannians, exploring their properties and symmetries in the context of $p$-adic matrices.

Contribution

It introduces and constructs $p$-adic Hua measures on inverse limits of Grassmannians, a novel extension of classical measures to the $p$-adic setting.

Findings

Construction of $p$-adic Hua measures

Identification of symmetry groups of these measures

Description of measure properties in the $p$-adic context

Abstract

We construct $p$-adic counterparts of Hua measures, measures on inverse limits of $p$-adic Grassmannians, and describe natural groups of symmetries of such measures.