权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Physical Combinatorics

物理组合学

基本信息

批准号：
13304010
负责人：
MIWA Tetsuji
金额：
$ 17.72万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

项目摘要

The main research results of the project consist of the following 5 parts.(i)We defined a filtration in the space of conformal coinvariants by using the degree defined by the representation at the infinity. We obtained a formula to represent the character of the associated gradedspace in terms of the Kostka polynomials. In this formula, we use the character of coinvariants for the fusion products. The obtained formulasare of fermionic type. We also obtained a bosonic formulas by solving a recursion relation.(ii)We constructed a basis of the space of symmetric polynomials satisfying a certain zero condition called the wheel condition by using the Jack and the Macdonald polynomials. This space is nothing but the minimal subrepresentation of the polynomial representation of the double affine Hecke algebra when it is reducible at the special values of the parameters.(iii)We realized the space of solutions to the system of difference equations which characterize the form factors of integrable quantum field theory, as an infinite dimensional homogeneous space in the representation theory of the quantum groups.(iv)We constructed a monomial basis of the minimal representations of the Virasoro algebra by using the Fourier components of the primary field and the quadratic relations satisfied by them.(v)Formulas in $n$-fold integrals for the $n$-point correlation functions of quantum spin chains are knwon. We obtained an algebraic formula without integrations by solving the qKZ difference equation. We used the transfer matrix with an auxiliary space of continuous dimensions. In the case of the XYZ model, we need the expression for the trace in Sklyanin's algebra. We proved that the calculation of the trace reduces to 7 elements in the algebra, and expressed thier traces by using elliptic theta functions.

本课题的主要研究成果包括以下五个部分。(i)We在共形共不变空间中定义了一个滤子，它是用无穷远处的表示所定义的度来定义的。得到了用Kostka多项式表示相应分次空间特征的公式。在这个公式中，我们使用的性质的共不变量的融合产品。所得到的公式是费米子型的。通过求解一个递推关系，得到了一个玻色子公式。（ii）利用Jack多项式和Macdonald多项式构造了对称多项式空间的一个基，该基满足称为轮条件的零条件。当双仿射Hecke代数的多项式表示在参数的特殊值处可约时，这个空间就是它的极小子表示。（iii）我们实现了描述可积量子场论的形式因子的差分方程系统的解的空间，作为量子群表示论中的无限维齐性空间。（iv）利用原域的Fourier分量及其满足的二次关系，构造了Virasoro代数的极小表示的单项式基。（v）已知量子自旋链的n点关联函数的n重积分公式。通过求解qKZ差分方程，得到了一个不含积分的代数公式.我们使用的转移矩阵与连续维的辅助空间。在XYZ模型的情况下，我们需要Sklyanin代数中的迹的表达式。证明了迹的计算可简化为代数中的7个元素，并用椭圆θ函数表示它们的迹。