On Hyperelliptic Abelian Functions of Genus 3

The affine ring A of the affine Jacobian variety of a hyperelliptic curve of genus 3 is studied as a D-module. The conjecture on the minimal D-free resolution previously proposed is proved in this case. As a by-product a linear basis of A is explicitly constructed in terms of derivatives of Klein's hyperelliptic pe functions.Comment: 40 page

Trace Construction of a Basis for the Solution Space of sl_N qKZ Equation

The trace of intertwining operators over the level one irreducible highest weight modules of the quantum affine algebra of type A_{N-1} is studied. It is proved that the trace function gives a basis of the solution space of the qKZ equation at a generic level. The highest-highest matrix element of the composition of intertwining operators is explicitly calculated. The integral formula for the trace is presented.Comment: 32 pages, Late

The Chiral Space of Local Operators in SU(2)-Invariant Thirring Model

The space of local operators in the SU(2) invariant Thirring model (SU(2) ITM) is studied by the form factor bootstrap method. By constructing sets of form factors explicitly we define a susbspace of operators which has the same character as the level one integrable highest weight representation of \hat{sl_2}. This makes a correspondence between this subspace and the chiral space of local operators in the underlying conformal field theory, the su(2) Wess-Zumino-Witten model at level one.Comment: 19 pages, typos are corrected, Accepted for publication in Comm. Math. Phy

On the Space of KdV Fields

The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring D generated by commuting derivations. A D-free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit of the construction in quantum integrable models assuming a certain conjecture. We propose another D-free resolution of A by extending the construction in the classical finite dimensional integrable system associated with a certain family of hyperelliptic curves to infinite dimension assuming a similar conjecture. The relation of two constructions is given.Comment: 13 page