Complex hypergeometric functions and integrable many-body problems

Abstract

General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. The derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable $N$-body systems emerging from particular degenerations of the elliptic Ruijsenaars and van Diejen models.

arXiv comment22 pp., published version

References in corpus (15)

• Discrete Heisenberg-Weyl Group and Modular Group
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Elliptic hypergeometry of supersymmetric dualities
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Current-Like Variables in Massive and Massless Integrable Models
• Properties of generalized univariate hypergeometric functions
• Exact solution of the Faddeev-Volkov model
• Unit circle elliptic beta integrals
• Elliptic hypergeometric functions
• On Complex Gamma-Function Integrals
• The Endless Beta Integrals
• A pair of commuting hypergeometric operators on the complex plane and bispectrality
• The rarefied elliptic Bailey lemma and the Yang-Baxter equation
• Hypergeometric rational approximations to $\zeta (4)$

Cited by in corpus (5)

• Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group
• On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions
• Complex and rational hypergeometric functions on root systems
• Complex rational Ruijsenaars model. The two-particle case
• Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry