Orderings on Calogero-Moser partition of imprimitive groups

TL;DR

This paper generalizes geometric and combinatorial orderings on irreducible representations of certain complex reflection groups, linking them with a- and c-functions, for broader parameter ranges and group types.

Contribution

It extends existing order constructions and their relations to a- and c-functions to all parameters and to the group G(l,e,n) when n is not divisible by e.

Findings

Extended order constructions to all parameters.

Established relations with a- and c-functions.

Generalized properties to G(l,e,n) for specific n.

Abstract

We extend to all parameters the constructions of the geometric and combinatorial orders on Irr G(l,1,n) due to I. Gordon, as well as the relations with the a and c-functions. This allows us to generalize these properties for the group G(l,e,n), at least when n is not divided by e.