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

DOI:
https://doi.org/10.1090/S0002-9947-00-02492-2

Published electronically:
June 14, 2000

MathSciNet review:
1665333

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Abstract | References | Similar Articles | Additional Information

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

MR Author ID:
349260

Email:
a.mathas@maths.usyd.edu.au

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