Algebraic study of integrable systems coming from field theories

研究了椭圆曲线上的非标准WZW模型--扭曲WZW模型。因式分解定理，它指出，层的共形块是局部自由的，甚至在边界的模空间的椭圆曲线退化到一个奇异的理性曲线，已被证明。共形块的层成为轨道WZW模型的层，特别地，如果在椭圆曲线上的标记点上插入可积表示，这个模型给出了有理共形场论的另一个例子，我还研究了以下相关的问题：1.有理模空间（一个有理函数空间）上可积系统的构造和推广。2.从边界共形场论的观点看Lower方程与无色散可积系统的关系。

I studied the "twisted WZW model", which is a non-standard WZW model on elliptic curves. The factorisation theorem, which states that the sheaf of conformal blocks is locally free even at the boundary of the moduli space where the elliptic curve degenerates to a singular rational curve, has been proved. The sheaf of conformal blocks becomes that of the orbifold WZW model.In particular, if one inserts integrable representations to marked points on the elliptic curve, this model gives another example of the rational conformal field theory.I studied the following related topics, too :1.Construction and generalisation of an integrable system on the monopole moduli space (a space of rational functions). Separation of variables of this system.2.Relation of the Lowner equations and dispersionless integrable systems, in view of the boundary conformal field theory.