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

DOI:
https://doi.org/10.1090/S1079-6762-01-00094-4

Published electronically:
June 26, 2001

MathSciNet review:
1852900

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We obtain a presentation of Schur algebras (and -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 of 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:
https://doi.org/10.1090/S1079-6762-01-00094-4

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