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.

22 pp., published version

References in corpus (5)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Properties of generalized univariate hypergeometric functions
• Exact solution of the Faddeev-Volkov model
• The Endless Beta Integrals

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