Jack Jia, University of Waterloo
Categories of representations of groups are well-behaved
They are abelian (behave like module categories), symmetric monoidal (have tensor products), every object has a dual and is semi-simple, to name a few. A natural question to ask is whether every category that exhibits similar behaviour is a representation category. Deligne proved a remarkable theorem that shows every symmetric tensor category with some imposed growth condition is in fact a category of representations. Moreover, he constructed some symmetric tensor categories with faster-than-exponential growth-these are so-called Deligne categories, which can be interpreted as complex rank analogs of classical representation categories. In this talk, I will introduce the notion of symmetric tensor categories, state Deligne’s Theorem, and construct some of the Deligne categories.
MC 5403