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Integral Schur algebras forGL 2

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Abstract

The structure of Schur algebrasS(2,r) over the integral domainZ is intensively studied from the quasi-hereditary algebra point of view. We introduce certain new bases forS(2,r) and show that the Schur algebraS(2,r) modulo any ideal in the defining sequence is still such a Schur algebra of lower degree inr. A Wedderburn-Artin decomposition ofS K (2,r) over a fieldK of characteristic 0 is described. Finally, we investigate the extension groups between two Weyl modules and classify the indecomposable Weyl-filtered modules for the Schur algebrasS Zp(2,r) withr<p 2.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Sydney, 2006, Sydney, NSW, Australia

    Jie Du

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  1. Jie Du
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Research supported by ARC Large Grant L20.24210

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Du, J. Integral Schur algebras forGL 2 . Manuscripta Math 75, 411–427 (1992). https://doi.org/10.1007/BF02567095

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  • DOI: https://doi.org/10.1007/BF02567095

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