Classification of horospherical invariant measures in higher rank: Teaser

TL;DR

This paper provides an accessible overview of classifying horospherical invariant measures in higher rank, focusing on a special case involving products of CAT(-1) spaces, simplifying complex arguments from prior work.

Contribution

It offers a simplified, expository version of classification results for horospherical invariant measures in a specific setting, making the complex theory more accessible.

Findings

Simplified classification of horospherical invariant measures in the special case

Clarification of key arguments from previous complex proofs

Focus on products of CAT(-1) spaces

Abstract

This is an expository/teaser version of [arXiv:2601.22668] for a very special case of products of $\mathrm{CAT}(-1)$ spaces. We keep this on arXiv as many parts of the argument of [arXiv:2601.22668] are simplified in this special case.