Structure and symmetries of integrable systems

可积系统的结构和对称性

基本信息

批准号：
05402001
负责人：
JIMBO Michio
金额：
$ 8.13万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (A)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1995
项目状态：
已结题

项目摘要

The major outcome of the present research project is as follows.1.Jimbo pushed forward the study of space of states of lattice models. Ising and RSOS type models were formulated in much the same way as for the vertex type models, and difference equations for correlations were derived. The theory was extended to spin chains with a boundary, and physical quantities were derived including vacuum states, energy and magnetization. For critical systems an integral formula for correlations was found. In representation theory, a new level 0 action was constructed on a level one module over the quantum affine algebra.2.Shiota constructed a notrivial solution to [P,Q] =P using a matrix integral similar to Kontsevich's. Takei showed, usuing the exact WKB analysis, that the Painleve I equation can be taken as a standard form near a simple turning point. He also constructed a general solution using the multiple scale anaysis.3.Umeda studied a new construction of a q-analog of differential operators, which appear in the Capelli identity for GLq (n) , in terms of classical q-difference operators. This opened up a connection with Gelfand-type hypergeometric equations.4.Ueno gave a concrete construction of projective flat connections on the vector bundles of conformal blocks over the moduli space of curves. Kono studied the free loop group of a compact simple Lie group, and found a connection between the mod p cohomology of the adjoint action of G on the closed loop group, and the integral cohomology of G.

本研究项目的主要成果如下： 1.Jimbo推进了晶格模型态空间的研究。 Ising 和 RSOS 类型模型的制定方式与顶点类型模型大致相同，并导出了相关性的差分方程。该理论被扩展到有边界的自旋链，并导出了包括真空态、能量和磁化强度在内的物理量。对于关键系统，找到了相关性的积分公式。在表示论中，在量子仿射代数的一级模块上构造了新的0级动作。2.Shiota使用类似于Kontsevich的矩阵积分构造了[P,Q]=P的非平凡解。 Takei 使用精确的 WKB 分析表明，Painleve I 方程可以视为简单转折点附近的标准形式。他还利用多尺度分析构造了一个通解。3.Umeda研究了微分算子的q-模拟的新构造，它出现在GLq(n)的Capelli恒等式中，用经典的q-差分算子来表示。这与Gelfand型超几何方程建立了联系。4.Ueno给出了曲线模空间上共形块向量束上射影平面连接的具体构造。 Kono 研究了紧简单李群的自由环群，发现了 G 在闭环群上的伴随作用的 mod p 上同调与 G 的积分上同调之间的联系。