On category O for the rational Cherednik algebra of G(m,1,n): the almost semisimple case

Richard Vale

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arXiv · math/0606523

On category O for the rational Cherednik algebra of G(m,1,n): the almost semisimple case

Richard Vale

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Abstract

We determine the structure of category $\cO$ for the rational Cherednik algebra of $G(m,1,n)$ in the case where the $\KZ$ functor satisfies a condition called \emph{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.

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Richard Vale. 2006-10-05. On category O for the rational Cherednik algebra of G(m,1,n): the almost semisimple case. https://arxiv.org/abs/math/0606523

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