## Journal of Mathematics of Kyoto University

### On category $\mathcal{O}$ for the rational Cherednik algebra of $G(m,1,n)$: the almost semisimple case

Richard Vale

#### 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.

#### Article information

Source
J. Math. Kyoto Univ., Volume 48, Number 1 (2008), 27-47.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250280974

Digital Object Identifier
doi:10.1215/kjm/1250280974

Mathematical Reviews number (MathSciNet)
MR2437890

Zentralblatt MATH identifier
1241.20007

#### Citation

Vale, Richard. On category $\mathcal{O}$ for the rational Cherednik algebra of $G(m,1,n)$: the almost semisimple case. J. Math. Kyoto Univ. 48 (2008), no. 1, 27--47. doi:10.1215/kjm/1250280974. https://projecteuclid.org/euclid.kjm/1250280974