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Article overview
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Cyclotomic $q$-Schur algebras associated to the Ariki-Koike algebra | | Toshiaki Shoji
; Kentaro Wada
; | | Date: |
12 Jul 2007 | | Abstract: | Let $S$ be the cyclotomic $q$-Schur algebra associated to the Ariki-Koike
algebra $H_{n,r}$ of rank $n$, introduced by Dipper-James-Mathas. For each $p =
(r_1, ..., r_g)$ such that $r_1 + ... + r_g = r$, we define a subalgebra $S^p$
of $S$ and its quotient algebra $ar S^p$. It is shown that $S^p$ is a
standardly based algebra and $ar S^p$ is a cellular algebra. By making use of
these algebras, we show that certain decomposition numbers for $S$ can be
expressed as a product of decomposition numbers for cyclotomic $q$-Schur
algebras associated to smaller Ariki_koike algebras $H_{n_k,r_k}$. | | Source: | arXiv, arxiv.0707.1733 | | Services: | Forum | Review | PDF | Favorites | |
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