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.

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).

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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