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

本研究项目的目的是分析椭圆可积系统，如八顶点或SOS模型。椭圆可积系统的困难源于电荷守恒定律的崩溃，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0级量子Knizhnik-Zamolodchikov方程。形状因数是最重要的量，因为如果你知道任何形状因数，就可以获得任何相关函数。夸诺在斯米尔诺夫公理方法的基础上得到了公式，使无反射点上的八顶点模型的S矩阵变为对角或反对角，从而简化了问题。在与M.Lashkevich的合作中，Quano证明了无反射点处的八顶点形状因子可以用theta函数的和来表示。合作者Nakayashiki将SU(2)不变的Thirring模型的局域场的手征空间作为局部运动积分的交换代数D上的模进行了研究。Nakayashiki证明了局部手征空间的性质给出了仿射李代数sl_2的1阶最高权表示的费米子公式。Nakayashiki与K.Cho合作研究了主极化交换簇J的交换函数空间作为J上整体全纯微分算子环D上的模。他们构造了一个无D的分解，以防theta除数是非奇异的。

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.