arXiv subjects
Publications and source records attributed to A. Nakayashiki.
The space of abelian functions of a principally polarized abelian variety J is studied as a module over the ring D of global holomorphic differential operators on J. We construct a D-free resolution in case the theta divisor is non-singular. As an application, in the case of dimension 2 and 3, we construct a new linear basis of the space of abelian functions in terms of logarithmic derivatives of the higher dimensional sigma function.
We show how to calculate the Euler characteristic of an affine Jacobi variety of a spectral curve from its defining equations.
We study the affine ring of the affine Jacobi variety of a hyper-elliptic curve. The matrix construction of the affine hyper-elliptic Jacobi varieties due to Mumford is used to calculate the character of the affine ring. By decomposing the character we make several conjectures on the cohomology groups of the affine hyper-elliptic Jacobi varieties. In the integrable system described by the family of these affine hyper-elliptic Jacobi varieties, the affine ring is closely related to the algebra of functions on the phase space, classical observables. We show that the affine ring is generated by the highest cohomology group over the action of the invariant vector fields on the Jacobi variety.
We discuss relations between different formulae for solutions of the Knizhnik-Zamolodchikov differential and the quantum Knizhnik-Zamolodchikov difference equations at level 0 and associated with rational solutions of the Yang-Baxter equation.
We propose that the correlation functions of the inhomogeneous eight vertex model in the anti-ferroelectric regime satisfy a system of difference equations with respect to the spectral parameters. Solving the simplest difference equation we obtain the expression for the spontaneous staggered polarization conjectured by Baxter and Kelland. We discuss also a related construction of vertex operators on the lattice.