Wednesday 15 January 2020, 15:30-16:30 in HG02.802
Damien Rivet (Université Clermont Auvergne)
Parabolically induced representations of semisimple quantum groups
First I will recall basic definitions about algebraic quantum groups and the link with classical groups illustrated with the example of SUq(2) and SLq(2,C). Then I will discuss principal series of representations of a complex semisimple quantum group G which are naturally induced from characters of the its Borel subgroup. I will present a general framework to adapt Rieffel induction procedure to quantum groups. By using the method developed by P. Clare for classical real semisimple group, we can build an induction module for G which gives a functor from the category of characters of the Levy factor of G into the category of representations of G. If time permits, I will present a way to build an analogous module for (the double cover of) SUq(1,1), inspired by recent work of E. Koelink on Mathieu modules.