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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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