Ivan Dimitrov
Queen´s University, Canada
Two Useful Functors in Representation Theory.
Abstract: A lot of interesting construction in Representation theory are given by functors - induction, tensor product, etc. In this talk I will introduce two less known functors and I will give some applications. The first one is the functor of locally finite vectors in a given representation. Its derived functor, known as Zuckerman's functor played a central role in the classification of Harish-Chandra modules. Here I will prove that it commutes with the tensor product functor, a property that may be useful in studying tensor categories of modules. The second functor that I will discuss is Mathieu's localization. It was used in the classification of weight modules over finite dimensional simple Lie algebras. I will show how it works for affine Lie algebras.