The BGG category O plays an important role in the study of representations of semisimple Lie algebras. Its connection to the Hecke category is a starting point of Geometric Representation Theory. In this lecture, I will introduce a version of category O for quantum groups at roots of unity. I will explain a derived equivalence from (the principal block of) quantum category O to the affine Hecke category. Under the equivalence, the highest weight structure of quantum category O provides a categorification of the “periodic Hecke module”.

I will continue in the second lecture by giving basic properties of quantum category O. Then I will introduce the affine Hecke algebra and the periodic Hecke module, and explain a categorification of the former using coherent sheaves on Steinberg variety.