On category O for the rational Cherednik algebra of G(m,1,n): the almost semisimple case
Abstract
We determine the structure of category for the rational Cherednik algebra of G(m,1,n) in the case where the 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.
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