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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