Integrable Hierarchies and Dispersionless Limit

Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical transformation, quantization of which is dressing operators of the ordinary KP and Toda hierarchy. An alternative construction of general solutions of the ordinary KP and Toda hierarchy is given as twistor construction which is quatization of the similar construction of solutions of dispersionless hierarchies. These results as well as those obtained in previous papers are presented with proofs and necessary technical details.Comment: 63 pages, University of Tokyo preprint, UTMS 94-35. (AMS TeX ver.2.1) (Typos are corrected and references are added.

Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. I

Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is described by the degeneration of the twisted WZW model on elliptic curves. The spaces of conformal blocks and conformal coinvariants of the degenerate model are factorised into those of the orbifold WZW model.Comment: 24 pages, 1 figure, contribution to ``Conformal Field Theory and Integrable Models'', Chernogolovka, Moscow Region, Russia, on September 15--21, 2002; typos corrected, references added (v2); typos corrected, final version (v3

Bosonization and integral representation of solutions of the Knizhnik-Zamolodchikov-Bernard equations

We construct an integral representation of solutions of the Knizhnik-Zamolodchikov-Bernard equations, using the Wakimoto modules.Comment: LaTeX2e, 24 pages; minor correction

Q-operators for higher spin eight vertex models with an even number of sites

We construct the Q-operator for generalised eight vertex models associated to higher spin representations of the Sklyanin algebra, following Baxter's 1973 paper. As an application, we prove the sum rule for the Bethe roots.Comment: 22 pages, Latex (amsart); revised (comments are added

Dispersionless BKP Hierarchy and Quadrant L\"owner Equation

We show that $N$-variable reduction of the dispersionless BKP hierarchy is described by a L\"owner type equation for the quadrant