Braided differential structure on Weyl groups, quadratic algebras and elliptic functions

Anatol N. Kirillov; Toshiaki Maeno

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arXiv · 0709.4599

Braided differential structure on Weyl groups, quadratic algebras and elliptic functions

Anatol N. Kirillov·Toshiaki Maeno

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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 $A,$ 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.

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BibTeX RIS

Anatol N. Kirillov, Toshiaki Maeno. 2007-10-01. Braided differential structure on Weyl groups, quadratic algebras and elliptic functions. https://arxiv.org/abs/0709.4599

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