Max filtering with reflection groups

TL;DR

This paper characterizes the minimal-distortion max filtering maps for reflection groups, providing insights into embedding orbit spaces of finite reflection groups into Euclidean space with low distortion.

Contribution

It identifies the max filtering maps of minimum distortion specifically for reflection groups, combining Coxeter classification and semidefinite programming techniques.

Findings

Characterization of minimal-distortion max filtering maps for reflection groups

Connection between Coxeter classification and semidefinite programming

Enhanced understanding of embeddings of orbit spaces into Euclidean space

Abstract

Given a finite-dimensional real inner product space V and a finite subgroup G of linear isometries, max filtering affords a bilipschitz Euclidean embedding of the orbit space V/G. We identify the max filtering maps of minimum distortion in the setting where G is a reflection group. Our analysis involves an interplay between Coxeter's classification and semidefinite programming.