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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn046, 23 pages, doi:10.1093/imrn/rnn046 published on May 19, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Braided Differential Structure on Weyl Groups, Quadratic Algebras, and Elliptic Functions

Anatol N. Kirillov1 and Toshiaki Maeno2

1 Research Institute for Mathematical Sciences
2 Department of Electrical Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan

Correspondence: Correspondence to be sent to: maeno{at}kuee.kyoto-u.ac.jp

We discuss a class of generalized divided difference operators which give rise to a representation of Nichols–Woronowicz algebras associated to Weyl groups. For the root system of type A, we also study the condition for the deformations of the Fomin–Kirillov quadratic algebra, which is a quadratic lift of the Nichols–Woronowicz algebra, to admit a representation given by generalized divided difference operators. The relations satisfied by the mutually commuting elements called Dunkl elements in the deformed Fomin–Kirillov algebra are determined. The Dunkl elements correspond to the truncated elliptic Dunkl operators via the representation given by the generalized divided difference operators.

Dedicated to the memory of Leonid Vaksman



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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
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Right arrow Articles by Maeno, T.
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