TL;DR
This paper investigates the BC_N Inozemtsev model, identifying finite-dimensional invariant spaces and demonstrating that conserved quantities preserve these spaces, with detailed analysis of the BC_2 case.
Contribution
It introduces finite-dimensional invariant spaces for the BC_N Inozemtsev model and shows conserved operators also preserve these spaces, advancing understanding of the model's structure.
Findings
Finite-dimensional invariant spaces are constructed for the BC_N Inozemtsev model.
Conserved quantities commute with the Hamiltonian and preserve these finite-dimensional spaces.
Detailed analysis provided for the BC_2 case.
Abstract
The BC_N Inozemtsev model is investigated. Finite-dimensional spaces which are invariant under the action of the Hamiltonian of the BC_N Inozemtsev model are introduced and it is shown that commuting operators of conserved quantities also preserve the finite-dimensional spaces. The BC_2 Inozemtsev model is studied in more detail.
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