Braided Differential Structure on Weyl Groups, Quadratic Algebras, and Elliptic Functions
書誌事項
- 公開日
- 2010-07-08
- DOI
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- 10.1093/imrn/rnn046
- 10.48550/arxiv.0709.4599
- 公開者
- Oxford University Press (OUP)
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説明
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.
収録刊行物
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- International Mathematics Research Notices
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International Mathematics Research Notices 2010-07-08
Oxford University Press (OUP)