Source identity and kernel functions for Inozemtsev-type systems

Abstract

The Inozemtsev Hamiltonian is an elliptic generalization of the differential operator defining the BC_N trigonometric quantum Calogero-Sutherland model, and its eigenvalue equation is a natural many-variable generalization of the Heun differential equation. We present kernel functions for Inozemtsev Hamiltonians and Chalykh-Feigin-Veselov-Sergeev-type deformations thereof. Our main result is a solution of a heat-type equation for a generalized Inozemtsev Hamiltonian which is the source for all these kernel functions. Applications are given, including a derivation of simple exact eigenfunctions and eigenvalues for the Inozemtsev Hamiltonian.

24 pages, 1 figure

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Cited by in corpus (6)

• Special polynomials related to the supersymmetric eight-vertex model: A summary
• Special polynomials related to the supersymmetric eight-vertex model. II. Schrödinger equation
• Source identities and kernel functions for deformed (quantum) Ruijsenaars models
• Series Solutions of the Non-Stationary Heun Equation
• Exact solutions by integrals of the non-stationary elliptic Calogero-Sutherland equation
• Source identities and kernel functions for the deformed Koornwinder-van Diejen models