On a conjecture about cellular characters for the complex reflection group G(d,1,n)

Data

• Title: On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$
• Authors: Abel Lacabanne
• arXiv link: https://arxiv.org/abs/1912.06427
• Published in: Ann. Math. Blaise Pascal 27 (2020) no. 1, 37-64.
• DOI: 10.4171/JCA/76)

Abstract

We propose a conjecture relating two different sets of characters for the complex reflection group $G(d,1,n)$. From one side, the characters are afforded by Calogero-Moser cells, a conjectural generalisation of Kazhdan-Lusztig cells for a complex reflection group. From the other side, the characters arise from a level $d$ irreducible integrable representations of $\mathcal{U}_{q}(\mathfrak{sl}_{\infty})$. We prove this conjecture in some cases: in full generality for $G(d,1,2)$ and for generic parameters for $G(d,1,n)$.

Citation

@article {MR4140870,
    AUTHOR = {Lacabanne, Abel},
     TITLE = {On a conjecture about cellular characters for the complex
              reflection group {$G(d, 1, n)$}},
   JOURNAL = {Ann. Math. Blaise Pascal},
  FJOURNAL = {Annales Math\'ematiques Blaise Pascal},
    VOLUME = {27},
      YEAR = {2020},
    NUMBER = {1},
     PAGES = {37--64},
      ISSN = {1259-1734,2118-7436},
   MRCLASS = {20F55 (20G42)},
  MRNUMBER = {4140870},
MRREVIEWER = {G\"otz\ Pfeiffer},
       URL = {http://ambp.cedram.org/item?id=AMBP_2020__27_1_37_0},
}