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ISSN 1079-6762

 

Generators and relations for Schur algebras


Authors: Stephen Doty and Anthony Giaquinto
Journal: Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 54-62
MSC (2000): Primary 16P10, 16S15; Secondary 17B35, 17B37
Published electronically: June 26, 2001
MathSciNet review: 1852900
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Abstract:

We obtain a presentation of Schur algebras (and $q$-Schur algebras) by generators and relations, one which is compatible with the usual presentation of the enveloping algebra (quantized enveloping algebra) corresponding to the Lie algebra $\mathfrak{gl}_n$ of $n\times n$ matrices. We also find several new bases of Schur algebras.


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Additional Information

Stephen Doty
Affiliation: Department of Mathematics, Loyola University, Chicago, IL 60626
Email: doty@math.luc.edu

Anthony Giaquinto
Affiliation: Department of Mathematics, Loyola University, Chicago, IL 60626
Email: tonyg@math.luc.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-01-00094-4
PII: S 1079-6762(01)00094-4
Keywords: Schur algebras, finite-dimensional algebras, enveloping algebras, quantized enveloping algebras
Received by editor(s): April 8, 2001
Published electronically: June 26, 2001
Communicated by: Alexandre Kirillov
Article copyright: © Copyright 2001 American Mathematical Society