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 theâ€¦ (More)

We diagonalize the transfer matrix of the inhomogeneous vertex models of the 6-vertex type in the anti-ferroelectric regime intoducing new types of q-vertex operators. The special cases of thoseâ€¦ (More)

An expression of the multivariate sigma function associated with a (n,s)-curve is given in terms of algebraic integrals. As a corollary the first term of the series expansion around the origin of theâ€¦ (More)

We prove that k-th singular cohomology group of the complement of the theta divisor in a hyperelliptic Jacobian is isomorphic to the k-th fundamental representation of the symplectic group Sp(2g,C).â€¦ (More)

We formulate the basic properties of q-vertex operators in the context of the Andrews-Baxter-Forrester (ABF) series, as an example of face-interaction models, derive the q-difference equationsâ€¦ (More)

The space of abelian functions of a principally polarized abelian variety (J, Î˜) is studied as a module over the ring D of global holomorphic differential operators on J . We construct a D freeâ€¦ (More)

Abstract. By using the KMN2 crystal base character formula for the basic A (1) 2 module, and the principally specialized Weyl-Kac character formula, we obtain a Rogers-Ramanujan type combinatorialâ€¦ (More)

The tau function corresponding to the affine ring of a certain plane algebraic curve, called (n, s)-curve, embedded in the universal Grassmann manifold is studied. It is neatly expressed by theâ€¦ (More)

We shall give an elementary and rigorous proof of the Thomae formula for ZN curves which was discovered by Bershadsky and Radul [1, 2]. Instead of using the determinant of the Laplacian we use theâ€¦ (More)