Seminars

 2.00 pm, Seminar Hall The category $\mathcal O$ for quantum groups Henning Haahr Andersen University of Aarhus, Denmark. 21-03-14 Abstract In their groundbreaking work in the $1970$'s Bernstein, Gelfand and Gelfand introduced the now famous category $\mathcal O$ for a semisimple Lie algebra $\mathfrak g$. The objects in this category are weight modules for $\mathfrak g$ whose weights have some upper bounds. One may consider the straightforward analogous category \mathcal O_q$for the quantized enveloping algebra$U_q(\mathfrak g)$. When$q$is generic it is well known that the "combinatorics", in particular the characters of the irreducible modules in$\mathcal O_q$coincide with the ones in$\mathcal O$. This is not so when$q$is a root of unity. In this talk - built on recent joint work with V. Mazorchuk - I shall explain how one may still give explicit descriptions of the irreducible modules, the projective modules and the tilting modules in$\mathcal O_q$when$q\$ is a complex root of unity.