Monomial bases for $q$-Schur algebras
Authors:
Jie Du and Brian Parshall
Journal:
Trans. Amer. Math. Soc. 355 (2003), 1593-1620
MSC (2000):
Primary 17B37, 20C08, 20G05
DOI:
https://doi.org/10.1090/S0002-9947-02-03188-4
Published electronically:
November 14, 2002
MathSciNet review:
1946407
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Using the Beilinson-Lusztig-MacPherson construction of the quantized enveloping algebra of $\mathfrak {gl}_n$ and its associated monomial basis, we investigate $q$-Schur algebras $\mathbf {S}_q(n,r)$ as βlittle quantum groups". We give a presentation for $\mathbf {S}_q(n,r)$ and obtain a new basis for the integral $q$-Schur algebra $S_q(n,r)$, which consists of certain monomials in the original generators. Finally, when $n\geqslant r$, we interpret the Hecke algebra part of the monomial basis for $S_q(n,r)$ in terms of Kazhdan-Lusztig basis elements.
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Additional Information
Jie Du
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia
MR Author ID:
242577
Email:
j.du@unsw.edu.au
Brian Parshall
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904-4137
MR Author ID:
136395
Email:
bjp8w@virginia.edu
Received by editor(s):
October 1, 2001
Received by editor(s) in revised form:
July 1, 2002
Published electronically:
November 14, 2002
Additional Notes:
Supported partially by ARC and NSF
Article copyright:
© Copyright 2002
American Mathematical Society
