Classification of charge-conserving loop braid representations

Abstract: The loop braid category is the diagonal category made up of loop braid groups $LB_n$, exactly paralleling the relationship between MacLane's braid category and the Artin braid groups. A loop braid representation is a monoidal functor from the loop braid category $\mathsf{L}$ to a suitable target category, and is $N$-charge-conserving if that target is the category $\mathrm{Match}^N$ of charge-conserving matrices. In this talk I will discuss the classification and construction of all such representations. (These representations fall into varieties indexed by a set in bijection with the set of pairs of plane partitions of total degree $N$.)

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.