From classes in the Weyl group to strata

TL;DR

This paper explores extending a known map from conjugacy classes to irreducible representations in Weyl groups to noncrystallographic Coxeter groups, aiming to understand the stratification of related algebraic structures.

Contribution

It provides evidence that the conjugacy class to representation map can be generalized beyond Weyl groups to noncrystallographic Coxeter groups.

Findings

The map from conjugacy classes to irreducible representations appears to extend naturally.

Supports the idea that stratification concepts apply to a broader class of Coxeter groups.

Lays groundwork for further exploration of algebraic structures in noncrystallographic settings.

Abstract

In a 2015 paper we have defined a map from the set of conjugacy classes in a Weyl group W to the set of irreducible representations of W (its image parametrizes the strata of a reductive group with Weyl group W). In this paper we provide evidence that this map makes sense even when W is replaced by a noncrystallographic Coxeter group.