Source identity and kernel functions for Inozemtsev-type systems
Mathematical Physics
2013-08-26 v1 math.MP
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.
Cite
@article{arxiv.1202.3544,
title = {Source identity and kernel functions for Inozemtsev-type systems},
author = {Edwin Langmann and Kouichi Takemura},
journal= {arXiv preprint arXiv:1202.3544},
year = {2013}
}
Comments
24 pages, 1 figure