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

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.

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