Elliptic quantum many-body problem and double affine Knizhnik-Zamolodchikov equation
Ivan Cherednik
TL;DR
This paper introduces an elliptic generalization of the Olshanetsky-Perelomov quantum many-body problem for arbitrary root systems and establishes its equivalence with a double affine Knizhnik-Zamolodchikov equation.
Contribution
It presents a new elliptic-matrix quantum problem and proves its equivalence to a double affine KZ equation for the first time.
Findings
Elliptic generalization of Dunkl operators for arbitrary root systems.
Equivalence between elliptic quantum problem and double affine KZ equation.
Framework for analyzing elliptic quantum many-body systems.
Abstract
The elliptic-matrix quantum Olshanetsky-Perelomov problem is introduced for arbitrary root systems by means of an elliptic generalization of the Dunkl operators. Its equivalence with the double affine generalization of the Knizhnik-Zamolodchikov equation (in the induced representations) is established.
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