On a conjecture about cellular characters for the complex reflection group $G\left(d,1,n\right)$
Annales Mathématiques Blaise Pascal, Tome 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 $G\left(d,1,n\right)$.

Publié le :
DOI : https://doi.org/10.5802/ambp.390
Classification : 20F55,  20G42
Mots clés : Cellular characters, Complex reflection groups
@article{AMBP_2020__27_1_37_0,
author = {Abel Lacabanne},
title = {On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$},
journal = {Annales Math\'ematiques Blaise Pascal},
pages = {37--64},
publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
volume = {27},
number = {1},
year = {2020},
doi = {10.5802/ambp.390},
language = {en},
url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.390/}
}
Abel Lacabanne. On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$. Annales Mathématiques Blaise Pascal, Tome 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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