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arXiv · 1202.3544

Source identity and kernel functions for Inozemtsev-type systems

Edwin Langmann·Kouichi Takemura
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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.

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Edwin Langmann, Kouichi Takemura. 2012-02-16. Source identity and kernel functions for Inozemtsev-type systems. https://doi.org/10.1063/1.4745001

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