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Howe duality and the quantum general linear group

Author(s): R. B. Zhang
Journal: Proc. Amer. Math. Soc. 131 (2003), 2681-2692.
MSC (2000): Primary 17B37, 20G42, 17B10
Posted: December 30, 2002
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Abstract: A Howe duality is established for a pair of quantized enveloping algebras of general linear algebras. It is also shown that this quantum Howe duality implies Jimbo's duality between ${\mathrm U}_q({\mathfrak{gl}}_n)$ and the Hecke algebra.

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Additional Information:

R. B. Zhang
Affiliation: School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia
Email: rzhang@maths.usyd.edu.au

DOI: 10.1090/S0002-9939-02-06892-2
PII: S 0002-9939(02)06892-2
Received by editor(s): June 24, 2001
Received by editor(s) in revised form: April 7, 2002
Posted: December 30, 2002
Communicated by: Dan M. Barbasch
Copyright of article: Copyright 2002, American Mathematical Society

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