Solvable Iattice models associated with supera I gebras and related topics

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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.