Elliptic Dunkl operators, root systems, and functional equations

V. M. Buchstaber; Giovanni Felder; A. V. Veselov

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arXiv · hep-th/9403178

Elliptic Dunkl operators, root systems, and functional equations

V. M. Buchstaber·Giovanni Felder·A. V. Veselov

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Abstract

We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases. In particular, solutions associated with elliptic curves are constructed. In the $A_{n-1}$ case, we discuss the relation with elliptic Calogero-Moser integrable $n$-body problems, and discuss the quantization ($q$-analogue) of our construction.

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V. M. Buchstaber, Giovanni Felder, A. V. Veselov. 1994-03-29. Elliptic Dunkl operators, root systems, and functional equations. https://arxiv.org/abs/hep-th/9403178

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