Transactions of the American Mathematical Society

Author(s): Jie Du; Brian Parshall
Journal: Trans. Amer. Math. Soc. 355 (2003), 1593-1620.
MSC (2000): Primary 17B37, 20C08, 20G05
Posted: November 14, 2002
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Abstract: Using the Beilinson-Lusztig-MacPherson construction of the quantized enveloping algebra of $\mathfrak{gl}_n$ and its associated monomial basis, we investigate

-Schur algebras $\mathbf{S}_q(n,r)$ as ``little quantum groups". We give a presentation for $\mathbf{S}_q(n,r)$ and obtain a new basis for the integral

-Schur algebra

, 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

in terms of Kazhdan-Lusztig basis elements.

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Jie Du
Affiliation: School of Mathematics, University of New South Wales, Sydney 2052, Australia
Email: j.du@unsw.edu.au

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