Analysis of elliptic integrable systems on the basis of CTM bootstrap approach

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The aim of the present research project is to analyze elliptic integrable systems such as eight-vertex or SOS model. The difficulty of elliptic integrable systems results from the breakdown of charge conservation law.The head investigator Quano constructed integral formulae for form factors of the cyclic SOS model, which solves the quantum Knizhnik-Zamolodchikov equation of level 0. Form factors are the most important quantities because any correlation functions can be obtained if you know any form factors. Quano obtained the formulae on the basis of Smirnov's axiomatic approach.The S-matrix of the eight-vertex model at reflectionless points becomes diagonal or anti-diagonal, so that the matter will be simplified. Quano showed that eight-vertex form factors at reflectionless points can be expressed in terms of the sum of theta functions in the joint work with M.Lashkevich.Co-investigator Nakayashiki studied the chiral space of local fields of SU(2)-invariant Thirring model as a module over the commutative algebra D of local integrals of motion. Nakayashiki showed that the character of the chiral space of local gives the fermionic formula of that of level 1 highest weight representation of affine Lie algebra sl_2 hat.Nakayashiki studied the space of abelian functions of a principally polarized abelian variety J as a module over the ring D of global holomorphic differential operators on J, in the joint work with K.Cho. They constructed a D-free resolution in case the theta divisor is non-singular.