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 dierential 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.
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Koji Cho, Andrey Mironov, Atsushi Nakayashiki, Baker–Akhiezer Modules on the Intersections of Shifted Theta Divisors. Publ. Res. Inst. Math. Sci. 47 (2011), no. 2, pp. 553–567DOI 10.2977/PRIMS/43