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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 $q$-Schur${}^{2}$ algebra


Authors: Jie Du and Leonard Scott
Journal: Trans. Amer. Math. Soc. 352 (2000), 4325-4353
MSC (2000): Primary 20C08, 20G05, 20C33
Published electronically: May 23, 2000
MathSciNet review: 1655991
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Abstract:

We study a class of endomomorphism algebras of certain $q$-permutation modules over the Hecke algebra of type $B$, whose summands involve both parabolic and quasi-parabolic subgroups, and prove that these algebras are integrally free and quasi-hereditary, and are stable under base change. Some consequences for decomposition numbers are discussed.


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Additional Information

Jie Du
Affiliation: School of Mathematics, University of New South Wales, Sydney 2052, Australia
Email: j.du@unsw.edu.au

Leonard Scott
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
Email: lls2l@virginia.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02262-5
PII: S 0002-9947(00)02262-5
Received by editor(s): March 3, 1997
Received by editor(s) in revised form: October 28, 1998
Published electronically: May 23, 2000
Additional Notes: The authors would like to thank ARC for support under the Large Grant A69530243 as well as NSF, and the Universities of Virginia and New South Wales for their cooperation. The first author also thanks the Newton Institute at Cambridge for its hospitality.
Article copyright: © Copyright 2000 American Mathematical Society