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arXiv · 1912.06427

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

Abel Lacabanne
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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 $G(d,1,n)$.

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BibTeXRIS

Abel Lacabanne. 2019-12-13. On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$. https://doi.org/10.5802/ambp.390

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