Skip Navigation

International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn046, 23 pages, doi:10.1093/imrn/rnn046 published on May 19, 2008
This Article
Right arrow Full Text (PDF)
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Kirillov, A. N.
Right arrow Articles by Maeno, T.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 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


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.