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.

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 𝒰 q (𝔰𝔩 ). We prove this conjecture in some cases: in full generality for G(d,1,2) and for generic parameters for G(d,1,n).

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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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