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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The modular representation theory of $ q$-Schur algebras


Author: Jie Du
Journal: Trans. Amer. Math. Soc. 329 (1992), 253-271
MSC: Primary 20C30; Secondary 16G99, 20G40
DOI: https://doi.org/10.1090/S0002-9947-1992-1022165-3
MathSciNet review: 1022165
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Abstract: We developed some basic theory of characteristic zero modular representations of $ q$-Schur algebras. We described a basis of the $ q$-Schur algebra in terms of the relative norm which was first introduced by P. Hoefsmit and L. Scott, and studied the product of two such basis elements. We also defined the defect group of a primitive idempotent in a $ q$-Schur algebra and showed that such a defect group is just the vertex of the corresponding indecomposable $ {\mathcal{H}_F}$-module.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1022165-3
Keywords: Hecke algebra, $ q$-Schur algebra, defect group, indecomposable module, vertex
Article copyright: © Copyright 1992 American Mathematical Society

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