Solvable Iattice models associated with supera I gebras and related topics

本文主要研究了超代数的可积模型。构造了Uq（sl(2 11)1）的Baxter q -算子，它们之间的泛函关系以及t -算子（转移矩阵）的wronskian型表达式。我们的公式既适用于格模型，也适用于共形场理论，因为它与算子作用的空间无关。将朗斯基型公式推广到Uq（gl(mn)A）情况，给出了t系统的朗斯基型解。它们是所谓的q（超级）字符的另一种形式。我第一次确定了Baxter q算子的个数为2A{M+N}。基于上述研究开发的技术，我们给出了粒子物理中AdS/CFT的t和q系统的解决方案。基于gl（M I N）的超特征生成函数的“协导”，给出了2A{M+N} Baxter q算子的新定义，并在不使用Bethe ansatz的情况下导出了Bethe ansatz方程。在算子的层面上阐明了孤子理论中的Backlund变换与Baxter q算子之间的关系。

We have researched on the following topics on integrable models related to superalgebras. We have constructed the Baxter Q-operators for Uq(sl(2 11)1), functional relations among them and Wronskian-type expressions of T-operators (transfer matrices). Our formulation can be applicable to both lattice models and conformal field theory since it is independent of the space where the operators act on.I made non-trivial generalization of Wronskian-type formulae to Uq(gl(M I N)A) case, and gave Wronskian-type solutions of the T-system. They are yet another form of the so-called q-(super)characters. I identified that the number of the Baxter Q-operators is 2A{M+N} for the first time.Based on the technique developed through the above research, we gave solutions to the T-and Q-systems for the AdS/CFT in particle physics.We proposed a new definition of the 2A{M+N} Baxter Q-operators based on 'co-derivative' on generating functions of supercharacters of gl(M I N), and derived the Bethe ansatz equations without using the Bethe ansatz. We also clarified relations between Backlund transformations in the soliton theory and the Baxter Q-operators on the level of operator.