On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta

The infinite number of particles limit in the dual to elliptic Ruijsenaars model (coordinate trigonometric degeneration of quantum double elliptic model) is proposed using the Nazarov-Sklyanin approach. For this purpose we describe double-elliptization of the Cherednik construction. Namely, we derive explicit expression in terms of the Cherednik operators, which reduces to the generating function of Dell commuting Hamiltonians on the space of symmetric functions. Although the double elliptic Cherednik operators do not commute, they can be used for construction of the N -> infinity limit.

Automated summary

This paper proposes the limitation of an infinite number of particles in the dual to elliptic Ruijsenaars model using the Nazarov-Sklyanin approach, and describes the double-elliptization of the Cherednik construction. It derives an explicit expression in terms of the Cherednik operators, reducing to the generating function of Dell commuting Hamiltonians on the space of symmetric functions. Despite the non-commutativity of the double elliptic Cherednik operators, they can still be utilized for constructing the N -> infinity limit.