Automorphisms of Products of Drinfeld Half Planes

TL;DR

This paper determines the automorphism groups of products of Drinfeld upper half-planes over different fields and establishes a rigidity theorem for their quotients by discrete torsion-free groups.

Contribution

It provides the first explicit description of automorphisms for products of Drinfeld half-planes over varying fields and proves a new rigidity result for their quotients.

Findings

Automorphism group of product of Drinfeld half-planes identified.

Rigidity theorem for quotients by discrete torsion-free groups established.

Results extend understanding of $p$-adic symmetric spaces.

Abstract

The Drinfeld upper half-planes play the role of symmetric spaces in the $p$-adic analytic world. We find the automorphism group of a product of such spaces, where each may be defined over a different field. We deduce a rigidity theorem for quotients of such products by discrete and torsion free groups.