Title: Lecture 2 Representation theory in non-integral rank
Speaker: Pavel Etingof (Massachusetts Institute of Technology)
Abstract: Examples of symmetric tensor categories over complex numbers which are not representation categories of supergroups were given by Deligne-Milne in 1981. These very interesting categories are interpolations of representation categories of classical groups GL(n), O(n), Sp(n) to arbitrary complex values of n. Deligne later generalized them to symmetric groups and also to characteristic p, where, somewhat unexpectedly, one needs to interpolate n to p-adic integer values rather than elements of the ground field. I will review some of the recent results on these categories and discuss algebra and representation theory in them.