Relaxed highest-weight modules over affine VOAs

2019/04/19 Fri 14:30 - 16:00

The (chiral) symmetry algebras of 2d conformal field theory are described as vertex operator algebras (VOAs).
Among them, C_2-cofinite ones with semisimple module categories correspond to
rational conformal field theory, whose characters span a SL_2(\Z)-invariant vector space
and whose fusion rules in module categories satisfy the celebrated Verlinde formula.

The affine VOAs are those construted by (and almost the same as) affine Kac-Moody algebras.
Among them, non-integrable affine VOAs are important examples of non-C_2-cofinite VOAs.
The Verlinde formula for non-integrable (admissible) affine VOAs proposed by T. Creutzig and D. Ridout
involves in relaxed highest-weight modules over affine Kac-Moody Lie algebras, which are modules parabolically
induced from weight modules over the associated finite-dimensional simple Lie algebras.

In this talk, we briefly review the Creutzig-Ridout theory and discuss recent progress on
character formulas and classification of relaxed highest-weight modules.
This talk is based on joint works with David Ridout.