Alejandro Ginory, Rutgers – Geometric Methods in Representation Theory Seminar

Title: The Verlinde Formula and Twisted Affine Lie Algebras 

Abstract: In the category of integrable highest weight modules for affine Lie algebras, the usual tensor product fails to preserve the so-called level (i.e., the scalar action of the canonical central element). For untwisted affine Lie algebras, a product structure called the fusion product makes the subcategory of modules at a fixed level into a braided monoidal category (in particular, with non-negative integral structure constants). In this talk, I will discuss a fusion product with integral structure constants on the space of characters of twisted affine Lie algebras. Surprisingly, in the A^(2)_{2r} case and for certain natural quotients for the other twisted cases, these algebras have negative structure constants “half” the time, (depending on the parity of the level). We will discuss these and other new features in the twisted cases, and their representation-theoretic meaning.