My major research interest is on the representation theory of quantum groups and its relations to the classical matrix groups. In particular, currently I am working on the class of positive principal series representations of split real quantum groups, which has a strong parallel to the theory of compact quantum groups.

The whole program involves several related theories, including Faddeev's modular double, the quantum dilogarithm and q-special functions, harmonic analysis on semigroup, cluster algebras, Lusztig's parametrization of total positivity, C*-algebra and unbounded operators. It is expected to have applications to construction of new Topological Quantum Field Theories (TQFT) and Categorifications.