On the research of a geometric realization of subfactors and its applications

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During the period of research, I obtained the following three results.(1) I constructed a geometric representation of the unitary group of a type II_1 factor with a subfactor.(2) For a Q-system associated with a subfactor, I defined the cohomology groups up to degree three via the method of deviation.(3) I constructed a new example of the increasing sequence of Weyl groups defined by Argerami-Stojanoff and showed that in the most of cases the Weyl groups are trivial.