| 研究実績の概要 |
In FT 2015, I continue the research on positive representations of split real quantum groups, as well as higher Teichmuller theory.
Using result from the positive Casimirs obtained in the previous year, we construct a continuous analogue of the tensor product decomposition of the split real sl2 from the compact case by using the idea of virtual highest weight vectors, which gives a promising way to generalize to higher rank. In a visit to I. Frenkel, several new ideas have been raised including the relation of the positive Casimir to simple singularities, and generalization of GL(2,C) to the split real case in the C*-algebraic setting.
In a visit to a winter school 2015 in Poland, category of positive representations and continuous analogue of TQFT was discussed with A. Ringel. Finally in a collaboration with A. Zeitlin we established the theory of higher Teichmuller theory in the case of super algebra Osp(2|2), where the results are in preparation for publishing.
|
