On Calogero-Moser cellular characters for imprimitive complex reflection groups

TL;DR

This paper explores the connection between Calogero-Moser cellular characters and Fock space characters, revealing new relationships with Lusztig's constructible characters and providing explicit character constructions for complex reflection groups.

Contribution

It introduces a novel interpretation linking Calogero-Moser cellular characters to Fock space vectors and explicitly constructs minimal $b$-invariant characters for complex reflection groups.

Findings

Lusztig's constructible characters are sums of Calogero-Moser cellular characters.

Explicit construction of minimal $b$-invariant characters for $G(l,1,n)$.

Established a new relationship between cellular characters and Fock space representations.

Abstract

We study the relationship between Calogero-Moser cellular characters and characters defined from vectors of a Fock space of type $A_{\infty}$. Using this interpretation, we show that Lusztig's constructible characters of the Weyl group of type $B$ are sums of Calogero-Moser cellular characters. We also give an explicit construction of the character of minimal $b$-invariant of a given Calogero-Moser family of the complex reflection group $G(l,1,n)$.