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Source identity and kernel functions for Inozemtsev-type systems. (English) Zbl 1278.81170
Summary: 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 of all these kernel functions. Applications are given, including a derivation of simple exact eigenfunctions and eigenvalues of the Inozemtsev Hamiltonian.