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

Algebraic Bethe Ansatz for XYZ Gaudin model

The eigenvectors of the Hamiltionians of the XYZ Gaudin model are constructed by means of the algebraic Bethe Ansatz. The construction is based on the quasi-classical limit of the corresponding results for the inhomogeneous higher spin eight vertex model.Comment: 11 pages, Latex file; minor correction

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

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.