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Lie Group Quantum Mathematics Seminar

Tensor structure on relaxed categories at admissible levels

Shashank Kanade, University of Denver

Location:  Hill 705
Date & time: Friday, 06 December 2019 at 12:00PM - 1:00PM

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.