Self-adjoint commuting differential operators and commutative subalgebras of the Weyl algebra
Mathematical Physics
2012-04-10 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
In this paper we study self-adjoint commuting ordinary differential operators. We find sufficient conditions when an operator of fourth order commuting with an operator of order is self-adjoint. We introduce an equation on coefficients of the self-adjoint operator of order four and some additional data. With the help of this equation we find the first example of commuting differential operators of rank two corresponding to a spectral curve of arbitrary genus. These operators have polynomial coefficients and define commutative subalgebras of the first Weyl algebra.
Keywords
Cite
@article{arxiv.1107.3356,
title = {Self-adjoint commuting differential operators and commutative subalgebras of the Weyl algebra},
author = {Andrey E. Mironov},
journal= {arXiv preprint arXiv:1107.3356},
year = {2012}
}