Elliptic Dunkl operators, root systems, and functional equations
High Energy Physics - Theory
2008-02-03 v1 Quantum Algebra
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 case, we discuss the relation with elliptic Calogero-Moser integrable -body problems, and discuss the quantization (-analogue) of our construction.
Cite
@article{arxiv.hep-th/9403178,
title = {Elliptic Dunkl operators, root systems, and functional equations},
author = {V. M. Buchstaber and Giovanni Felder and A. V. Veselov},
journal= {arXiv preprint arXiv:hep-th/9403178},
year = {2008}
}
Comments
30 pages