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On decomposition numbers with Jantzen filtration of cyclotomic $q$-Schur
algebras | | Kentaro Wada
; | | Date: |
12 Jul 2007 | | Abstract: | Let $Sc(vL)$ be the cyclotomic $q$-Schur algebra associated to the
Ariki-Koike algebra $He_{n,r}$, introduced by Dipper-James-Mathas. In this
paper, we consider $v$-decomposition numbers of $Sc(vL)$, namely
decomposition numbers with respect to the Jantzen filtrations of Weyl modules.
We prove, as a $v$-analogue of the result obtained by Shoji-Wada, a product
formula for $v$-decomposition numbers of $Sc(vL)$, which asserts that certain
$v$-decomposition numbers are expressed as a product of $v$-decomposition
numbers for various cyclotomic $q$-Schur algebras associated to Ariki-koike
algebras $He_{n_i,r_i}$ of smaller rank. Moreover we prove a similar formula
for $v$-decomposition numbers of $He_{n,r}$ by using a Schur functor. | | Source: | arXiv, arxiv.0707.1753 | | Services: | Forum | Review | PDF | Favorites | |
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