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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Jantzen sum formula for cyclotomic $q$-Schur algebras


Authors: Gordon James and Andrew Mathas
Journal: Trans. Amer. Math. Soc. 352 (2000), 5381-5404
MSC (2000): Primary 16G99; Secondary 20C20, 20G05
Published electronically: June 14, 2000
MathSciNet review: 1665333
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Abstract:

The cyclotomic $q$-Schur algebra was introduced by Dipper, James and Mathas, in order to provide a new tool for studying the Ariki-Koike algebra. We here prove an analogue of Jantzen's sum formula for the cyclotomic $q$-Schur algebra. Among the applications is a criterion for certain Specht modules of the Ariki-Koike algebras to be irreducible.


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Additional Information

Gordon James
Affiliation: Department of Mathematics, Imperial College, Queen’s Gate, London SW7 2BZ, United Kingdom
Email: g.james@ic.ac.uk

Andrew Mathas
Affiliation: School of Mathematics, University of Sydney, Sydney NSW 2006, Australia
Email: a.mathas@maths.usyd.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02492-2
PII: S 0002-9947(00)02492-2
Received by editor(s): March 18, 1998
Received by editor(s) in revised form: December 1, 1998
Published electronically: June 14, 2000
Additional Notes: The authors would like to thank the Isaac Newton Institute for its hospitality. The second author also gratefully acknowledges the support of the Sonderforschungsbereich 343 at the Universität Bielefeld.
Article copyright: © Copyright 2000 American Mathematical Society