Calendar

Shashank Kanade, University of Denver

• Abstract:  Representation theory of vertex operator algebras based on affine Lie algebras at admissible (yet non-integral) levels is quite rich. Here, the underlying VOAs are non-rational. A culmination of various deep results of Arakawa, Creutzig--Huang--Yang and Creutzig is that the sub-category of ordinary modules is finite, vertex tensor, rigid (at least in the simply-laced case) and often (but not always) a modular category. However, many considerations necessitate looking at a (much) bigger non-finite category containing the so-called relaxed highest-weight modules. In an ongoing joint work with David Ridout, we are looking at the vertex tensor structure on these relaxed categories. I will present a few preliminary results obtained (only for sl_2!) in this direction.