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On Calogero–Moser cellular characters for imprimitive complex reflection groups

Nicolas Jacon and Abel Lacabanne

Vol. 5 (2023), No. 4, 605–625
Abstract

We study the relationship between Calogero–Moser cellular characters and characters defined from vectors of a Fock space of type A. 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).

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