Ricci curvature of Bruhat orders

TL;DR

This paper investigates the Ricci curvature of Hasse diagrams of Bruhat orders in finite Coxeter groups, introducing a new graph to facilitate the analysis and computing maximum degrees for specific types.

Contribution

It introduces a novel graph construction for elements in Coxeter groups and computes maximum degrees of Bruhat order graphs for types B and D.

Findings

Maximum degree computed for type B and D Bruhat graphs.

Introduction of a new graph () for elements in Coxeter groups.

Insights into Ricci curvature properties of Bruhat orders.

Abstract

We study the Ricci curvature of the Hasse diagrams of the Bruhat order of finite irreducible Coxeter groups. For this purpose we compute the maximum degree of these graphs for types $B_n$ and $D_n$. The proof uses a new graph $\Gamma(\pi)$ defined for any element $\pi$ in the corresponding group.