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
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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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DG S. Doty and A. Giaquinto, Presenting Schur algebras as quotients of the universal enveloping algebra of $\mathfrak {gl}_2$, Algebras and Representation Theory, to appear.
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DG S. Doty and A. Giaquinto, Presenting Schur algebras as quotients of the universal enveloping algebra of $\mathfrak {gl}_2$, Algebras and Representation Theory, to appear.
DGquantum S. Doty and A. Giaquinto, Presenting quantum Schur algebras as quotients of the quantized enveloping algebra of $\mathfrak {gl}_2$, preprint, Loyola University Chicago, December 2000.
PSA S. Doty and A. Giaquinto, Presenting Schur algebras, preprint, Loyola University Chicago, April 2001.
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Green J. A. Green, Polynomial Representations of $\mathsf {GL}_n$ (Lecture Notes in Math. 830), Springer-Verlag, New York 1980.
RGreen R. Green, $q$-Schur algebras as quotients of quantized enveloping algebras, J. Algebra 185 (1996), 660–687.
Jimbo M. Jimbo, A $q$-analogue of $U(\mathfrak {gl}(N+1))$, Hecke algebra, and the Yang-Baxter equation, Letters Math. Physics 11 (1986), 247–252.
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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
