On commutative subalgebras of the Weyl algebra that are related to commuting operators of arbitrary rank and genus

Abstract

We construct examples of commuting ordinary scalar differential operators with polynomial coefficients that are related to a spectral curve of an arbitrary genus g and to an arbitrary even rank r = 2k, and also to an arbitrary rank of the form r = 3k, of the vector bundle of common eigenfunctions of the commuting operators over the spectral curve.