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

本课题的目的是研究椭圆型可积系统，如八顶点或SOS模型。椭圆可积系统的困难是由于电荷守恒定律的破坏。首席研究员Quano构造了循环SOS模型的形状因子的积分公式，该公式求解了水平0的量子Knizhnik-Zamolodchikov方程。形状因子是最重要的量，因为如果您知道任何形状因子，就可以获得任何相关函数。Quano在Smirnov公理化方法的基础上得到了公式，八顶点模型在无反射点处的S-矩阵变为对角或反对角，从而使问题得到简化。Quano在与M.Lashkevich的联合工作中证明了无反射点处的八顶点形状因子可以用θ函数的和来表示。共同研究员Nakayashiki研究了SU（2）-不变Thirring模型的局部场的手征空间作为局部运动积分的交换代数D上的模。Nakayashiki表明，字符的手征空间的地方给出了费米子公式的水平1最高的重量表示的仿射李代数sl_2帽子。Nakayashiki研究了空间的交换函数的主要极化交换品种J作为一个模块在环D的全球全纯微分算子J，在联合工作与K. Cho。他们构造了一个D-自由的解决方案的情况下，θ因子是非奇异的。

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.