## The Jantzen sum formula for cyclotomic $q$–Schur algebras

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- by Gordon James and Andrew Mathas
- Trans. Amer. Math. Soc.
**352**(2000), 5381-5404 - DOI: https://doi.org/10.1090/S0002-9947-00-02492-2
- Published electronically: June 14, 2000
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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.## References

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## Bibliographic 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.
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1665333