Algebraic study of integrable systems coming from field theories

我研究了“扭曲WZW模型”，这是椭圆曲线上的非标准WZW模型。证明了保形块束即使在椭圆曲线退化为奇异有理曲线的模空间边界处也是局部自由的分解定理。共形块体的轴变成了WZW型的轨道轴。特别地，如果在椭圆曲线上的标记点上插入可积表示，则该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主题：1。单极模空间（有理函数空间）上可积系统的构造与推广。本系统的变量分离基于边界共形场理论的低纳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.