Speaker
Anna Lachowska
Description
Since their invention over 30 years ago, quantum groups and their representations have been playing an important role in mathematical physics. To each semisimple Lie algebra g and a root of unity q,
one can associate the Lusztig’s “divided powers” quantum group at a root of unity. The category of its finite dimensional representations over complex numbers is non-semisimple and has a remarkable tensor subcategory, which leads in particular to the definition of the fusion category. It also changes the standard result about the multiplicity of a given finite dimensional representation in a tensor power of a standard representation. I will review some recent results in this area and discuss applications.
