On a conjecture about cellular characters for the complex reflection group $G\left(d,1,n\right)$
Annales mathématiques Blaise Pascal, Volume 27 (2020) no. 1, pp. 37-64.

We propose a conjecture relating two different sets of characters for the complex reflection group $G\left(d,1,n\right)$. 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 ${𝒰}_{q}\left({\mathrm{𝔰𝔩}}_{\infty }\right)$. We prove this conjecture in some cases: in full generality for $G\left(d,1,2\right)$ and for generic parameters for $G\left(d,1,n\right)$.

Published online:
DOI: 10.5802/ambp.390
Classification: 20F55, 20G42
Keywords: Cellular characters, Complex reflection groups
Abel Lacabanne 1

1 Institut de Recherche en Mathématique et Physique Université Catholique de Louvain Chemin du Cyclotron 2 1348 Louvain-la-Neuve, Belgium
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Abel Lacabanne. On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$. Annales mathématiques Blaise Pascal, Volume 27 (2020) no. 1, pp. 37-64. doi : 10.5802/ambp.390. https://ambp.centre-mersenne.org/articles/10.5802/ambp.390/

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