On the eigenvalues of p-adic curvature

TL;DR

This paper investigates the eigenvalues of p-adic curvature transformations on Bruhat-Tits buildings, providing precise maximal eigenvalues and near-optimal bounds for the smallest non-zero eigenvalues, advancing understanding of their spectral properties.

Contribution

It determines the maximal eigenvalue and offers an essentially optimal upper bound for the minimal non-zero eigenvalue of p-adic curvature transformations on Bruhat-Tits buildings.

Findings

Maximal eigenvalue of p-adic curvature transformations is explicitly determined.

An essentially optimal upper bound for the minimal non-zero eigenvalue is established.

Results enhance understanding of spectral properties of p-adic curvature transformations.

Abstract

We determine the maximal eigenvalue of the p-adic curvature transformations on Bruhat-Tits buildings, and we give an essentially optimal upper bound on the minimal non-zero eigenvalue of these transformations.