Baker-Akhiezer modules on the intersections of shifted theta divisors

The restriction, on the spectral variables, of the Baker-Akhiezer (BA) module of a g- dimensional principally polarized abelian variety with the non-singular theta divisor to an intersection of shifted theta divisors is studied. It is shown that the restriction to a k-dimensional variety becomes a free module over the ring of differential operators in k variables. The remaining g - k derivations dene evolution equations for generators of the BA-module. As a corollary new examples of commutative rings of partial differential operators with matrix coecients and their non-trivial evolution equations are obtained.