Braided differential structure on Weyl groups, quadratic algebras and elliptic functions
Quantum Algebra
2007-10-01 v2
Abstract
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 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.
Cite
@article{arxiv.0709.4599,
title = {Braided differential structure on Weyl groups, quadratic algebras and elliptic functions},
author = {Anatol N. Kirillov and Toshiaki Maeno},
journal= {arXiv preprint arXiv:0709.4599},
year = {2007}
}