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

Vale, Richard

Vale, Richard

J. Math. Kyoto Univ., Tome 48 (2008) no. 4, p. 27-47 / Harvested from Project Euclid

Résumé

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.

Publié le : 2008-05-15
Classification:

@article{1250280974,
     author = {Vale, Richard},
     title = {On category $\mathcal{O}$ for the rational Cherednik algebra of $G(m,1,n)$: the almost semisimple case},
     journal = {J. Math. Kyoto Univ.},
     volume = {48},
     number = {4},
     year = {2008},
     pages = { 27-47},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250280974}
}

Vale, Richard. On category $\mathcal{O}$ for the rational Cherednik algebra of $G(m,1,n)$: the almost semisimple case. J. Math. Kyoto Univ., Tome 48 (2008) no. 4, pp.  27-47. http://gdmltest.u-ga.fr/item/1250280974/