Modified Ariki-Koike algebras and cyclotomic q-Schur algebras
详细信息 查看全文
- 作者：Nobuharu Sawada and Toshiaki Shoji
- 刊名：Mathematische Zeitschrift
- 出版年：2005
- 出版时间：April 2005
- 年：2005
- 卷：249
- 期：4
- 页码：829-867
- 全文大小：421 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Springer Berlin / Heidelberg
- ISSN：1432-1823
文摘
The modified Ariki-Koike algebra is a variation of the original Ariki-Koike algebra over an integral domain R. When R is a rational function field over the independent parameters, But for general R, is not isomorphic to , and has a simpler structure than . In this paper, we construct a cellular basis of which has a similar property as the cellular basis of introduced by Dipper-James-Mathas. By comparing these two cellular bases, we obtain some estimate on the decomposition numbers of in terms of the decomposition numbers of . We also prove the integral form of the Schur-Weyl reciprocity between a certain quantum algebra Uq and on the tensor space