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

Author(s): Jie Du; Leonard Scott
Journal: Trans. Amer. Math. Soc. 352 (2000), 4325-4353.
MSC (2000): Primary 20C08, 20G05, 20C33
Posted: May 23, 2000
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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: 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
Posted: 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.
Copyright of article: Copyright 2000, American Mathematical Society

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