Unoriented 2-dimensional TQFTs and the category Rep(S_t \wr Z_2)

Abstract: Let k be an algebraically closed field of characteristic zero. The category of oriented 2-dimensional cobordisms can be understood in purely algebraic terms via a description by generators and relations; moreover, it is possible to recover from it the Deligne category Rep(S_t), which interpolates the category of finite-dimensional representations of the symmetric group S_n from n a positive integer to any parameter t in k. We show an analogous story happens in the unoriented case: via its description by generators and relations, we recover the generalized Deligne category Rep(S_t \wr Z_2), which interpolates the category of finite-dimensional representations of the wreath product S_t \wr Z_2.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home