Lectures: Tuesdays 14:00 to 16:00 in Kleiner Hörsaal

Abstract: Deligne constructed symmetric tensor categories interpolating the categories of representations of the symmetric groups in characteristic zero. Deligne's interpolation categories were amongst the first examples of symmetric tensor categories not arising from an algebraic (super-)group, i.e. going beyond classical representation theory.

Recently, Harman and Snowden put this construction into a much broader framework, which takes as input an oligomorphic group equipped with a suitable measure.

The goal of this course is to go over this general construction, and examine some examples in detail.

In particular, Deligne's interpolation categories are recovered from the infinite symmetric group and its family of measures.

Moreover, perhaps the most remarkable example is the Delannoy category, which arises from the group of orientation preserving automorphisms of the real line. Time permitting, we will examine this example in detail following the work of Harman, Snowden, and Snyder.