Abstract: |
We review the notion of positive representations of split real quantum groups introduced in a joint work with Igor Frenkel, and describe the tensor product decomposition when restricted to the Borel part, through the use of multiplier Hopf algebra. This generalized the essential step of the construction of the quantum Teichmuller theory from the representation of the quantum plane studied by Frenkel-Kim, and provide a candidate for the quantum higher Teichmuller theory. This is an on going joint work with Hyun-Kyu Kim. |