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 Free Access

Abstract | References | Similar Articles | Additional Information

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

MR Author ID:
59395

ORCID:
0000-0003-3927-3009

Email:
doty@math.luc.edu

**Anthony Giaquinto**

Affiliation:
Department of Mathematics, Loyola University, Chicago, IL 60626

Email:
tonyg@math.luc.edu

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