Higher order deformed elliptic Ruijsenaars operators

Abstract

We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of operators was previously introduced by Feigin and Silantyev. They provide a quantum mechanical description of two kinds of relativistic quantum mechanical particles which can be identified with particles and anti-particles in an underlying quantum field theory. We give direct proofs of the commutativity of our operators and of some other fundamental properties such as kernel function identities. In particular, we give a rigorous proof of the quantum integrability of the deformed Ruijsenaars model.

29 pages

References in corpus (6)

• Duality in elliptic Ruijsenaars system and elliptic symmetric functions
• Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture
• Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation
• An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type $A$
• New transformations for elliptic hypergeometric series on the root system An
• From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators

Cited by in corpus (3)

• Conformal field theory, solitons, and elliptic Calogero--Sutherland models
• Wall-crossing for vortex partition function and handsaw quiver varierty
• $K$-theoretic wall-crossing formulas and multiple basic hypergeometric series