Cyclotomic Schur algebras associated to the ArikiKoike algebra
Authors:
Toshiaki Shoji and Kentaro Wada
Journal:
Represent. Theory 14 (2010), 379416
MSC (2010):
Primary 20C08, 20G43
Published electronically:
May 6, 2010
MathSciNet review:
2644457
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Abstract: Let be the ArikiKoike algebra associated to the complex reflection group , and let be the cyclotomic Schur algebra associated to , introduced by Dipper, James and Mathas. For each such that , we define a subalgebra of and its quotient algebra . It is shown that is a standardly based algebra and is a cellular algebra. By making use of these algebras, we prove a product formula for decomposition numbers of , which asserts that certain decomposition numbers are expressed as a product of decomposition numbers for various cyclotomic Schur algebras associated to ArikiKoike algebras of smaller rank. This is a generalization of the result of N. Sawada. We also define a modified ArikiKoike algebra of type , and prove the SchurWeyl duality between and .
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Additional Information
Toshiaki Shoji
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusaku, Nagoya 4648602, Japan
Kentaro Wada
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusaku, Nagoya 4648602, Japan
Address at time of publication:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 6068502 Japan
DOI:
http://dx.doi.org/10.1090/S1088416510003754
PII:
S 10884165(10)003754
Received by editor(s):
November 1, 2007
Received by editor(s) in revised form:
February 6, 2010
Published electronically:
May 6, 2010
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
