Elliptic Dunkl operators, root systems, and functional equations

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

Elliptic Dunkl operators, root systems, and functional equations

高能物理 - 理论 2008-02-03 v1 量子代数

作者: V. M. Buchstaber , Giovanni Felder , A. V. Veselov

摘要

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.

关键词

calogero models operator theory and quantum mechanics boson normal ordering

引用

@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}
}

备注

30 pages

Elliptic Dunkl operators, root systems, and functional equations

摘要

关键词

引用

备注

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