University of Sydney Algebra Seminar
David Ridout
Friday 17 November, 12-1pm, Place: Carslaw 173
Logarithmic Kazhdan--Lusztig correspondences
The Kazhdan--Lusztig correspondence is an equivalence of braided tensor categories dating back to a series of papers that appeared in JAMS from 1993-94. On one side is a category of representations of an untwisted affine Kac--Moody algebra, equipped with the fusion product of conformal field theory, and the other is a category of representations of an associated quantum group, equipped with the usual tensor product.
It is natural to replace ``untwisted affine Kac--Moody algebra'' with ``affine vertex operator algebra''. Work in this direction originally concentrated on cases in which there is a natural VOA category that is finite and semisimple. However, the quantum group category is neither, unless one artificially semisimplifies. Today, I'd like to say a few words about what can say (and do) if we don't semisimplify.