Self-adjoint commuting ordinary differential operators

• 成果类型: Article
• 署名作者: Mironov, Andrey E.
• 署名单位: Russian Academy of Sciences; Sobolev Institute of Mathematics; Lomonosov Moscow State University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0486-8
• 发表日期: 2014
• 页码: 417-431
• 关键词: elliptic-curves; EQUATIONS; genus-2

摘要

In this paper we study self-adjoint commuting ordinary differential operators of rank two. We find sufficient conditions when an operator of fourth order commuting with an operator of order 4g+2 is self-adjoint. We introduce an equation on potentials V(x),W(x) of the self-adjoint operator 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 higher genus. These operators have polynomial coefficients and define commutative subalgebras of the first Weyl algebra.