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Generators and relations for Schur algebras
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Generators and relations for Schur algebras
Stephen Doty and Anthony Giaquinto
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 $\gl_n$ of $n\times n$ matrices. We
also find several new bases of Schur algebras.
Copyright 2001 American Mathematical Society
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Article Info
- ERA Amer. Math. Soc. 07 (2001), pp. 54-62
- Publisher Identifier: S 1079-6762(01)00094-4
- 2000 Mathematics Subject Classification. Primary 16P10, 16S15; Secondary 17B35, 17B37
- Key words and phrases. Schur algebras, finite-dimensional algebras, enveloping algebras, quantized enveloping algebras
- Received by the editors April 8, 2001
- Posted on June 26, 2001
- Communicated by Alexandre Kirillov
- Comments (When Available)
Stephen Doty
Department of Mathematics, Loyola University, Chicago, IL 60626
E-mail address: doty@math.luc.edu
Anthony Giaquinto
Department of Mathematics, Loyola University, Chicago, IL 60626
E-mail address: tonyg@math.luc.edu
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