Abstract
We determine the structure of category $\mathcal{O}$ for the rational Cherednik algebra of the wreath product complex reflection group $G(m,1,n)$ in the case where the $\mathsf{KZ}$ functor satisfies a condition called separating simples. As a consequence, we show that the property of having exactly $N-1$ simple modules, where $N$ is the number of simple modules of $G(m,1,n)$, determines the Ariki-Koike algebra up to isomorphism.
Citation
Richard Vale. "On category $\mathcal{O}$ for the rational Cherednik algebra of $G(m,1,n)$: the almost semisimple case." J. Math. Kyoto Univ. 48 (1) 27 - 47, 2008. https://doi.org/10.1215/kjm/1250280974
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