On Calogero-Moser cellular characters for imprimitive complex reflection groups

Data

• Title: On Calogero-Moser cellular characters for imprimitive complex reflection groups
• Authors: Nicolas Jacon and Abel Lacabanne
• arXiv link: https://arxiv.org/abs/2204.01014
• Published in: Tunis. J. Math. 5 (2023), no.4, 605–625.
• DOI: 10.2140/tunis.2023.5.605

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 $G(l,1,n)$.

Citation

@article {MR4669152,
    AUTHOR = {Jacon, Nicolas and Lacabanne, Abel},
     TITLE = {On {C}alogero-{M}oser cellular characters for imprimitive
              complex reflection groups},
   JOURNAL = {Tunis. J. Math.},
  FJOURNAL = {Tunisian Journal of Mathematics},
    VOLUME = {5},
      YEAR = {2023},
    NUMBER = {4},
     PAGES = {605--625},
      ISSN = {2576-7658,2576-7666},
   MRCLASS = {20C08 (20F55 20G42)},
  MRNUMBER = {4669152},
       DOI = {10.2140/tunis.2023.5.605},
       URL = {https://doi.org/10.2140/tunis.2023.5.605},
}