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

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

2006-06-21

arxiv.org/abs/math/0606523v3

Mathematics

Representation Theory

24 pages, new section added

Scientific paper

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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