Title: Classifying Unitary Modules for Generalized TLJ
Speaker: Giovanni Ferrer - University of Puerto Rico Mayaguez
Abstract: Generalized Temperley-Lieb-Jones (TLJ) *-2-categories associated to weighted graphs were introduced in unpublished work of Morrison and Walker. We will go over the construction of these graph-generated TLJ *-2-categories and introduce a corresponding notion of unitary modules. In joint work with Hern\'andez-Palomares, we provide a classification of these modules in terms of weighted graphs in the spirit of Yamagami's classification of fiber functors on TLJ categories and DeCommer and Yamashita's classification of unitary modules for ${\rm Rep(SU}_q(2))$. We will discuss these classification projects and the relations between them.
