Commutative rings of differential operators connected with two-dimensional Abelian varieties (Q1595494)

In the early 90's Nakayashiki realized an idea by Sato and proved the existence of commutative rings of matrix differential operators which have a finite gap on all levels of energy and whose Floquet-Bloch functions are parametrized by the complements to the theta-divisors in generic Abelian varieties. The Nakayashiki construction of such operators is based on the Fourier-Mukai transformation. In the article under review, the author finds explicit formulas for such operators related to two-dimensional Abelian varieties in terms of theta-functions of these varieties.