Chennai Mathematical Institute


2.00 pm, Seminar Hall
The category $\mathcal O$ for quantum groups

Henning Haahr Andersen
University of Aarhus, Denmark.


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.