On Calogero–Moser cellular characters for imprimitive complex reflection groups

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 $G (l, 1, n)$ .

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Keywords

imprimitive complex reflection groups, Calogero–Moser cellular characters, Fock space

Mathematical Subject Classification

Primary: 20C08

Secondary: 20G42

Milestones

Received: 4 July 2022

Revised: 3 May 2023

Accepted: 8 June 2023

Published: 21 November 2023

Authors

Nicolas Jacon
UFR Sciences Exactes et Naturelles Laboratoire de Mathématiques Université de Reims Champagne-Ardenne Reims France

Abel Lacabanne
Laboratoire de Mathématiques Blaise Pascal Université Clermont Auvergne Campus des Cézeaux Aubière France

Vol. 5, No. 4, 2023

Nicolas Jacon and Abel Lacabanne

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors