Emmy-Noether-Seminar: Tensor structures for affine Lie algebras at positive levels

Tensor structures for affine Lie algebras at positive levels

Jonathan Gruber (FAU)

Abstract: An affine Lie algebra g is a central extension of the loop algebra of a complex simple Lie algebra, and a g-module is said to have (relative) level k if the canonical central element acts by the scalar k-h, where h is the dual Coxeter number. For all levels k that are not positive rational or zero, Kazhdan and Lusztig have defined a braided monoidal structure on a parabolic BGG category O of g-modules of level k. In this talk, I will explain the definition of a braided monoidal structure on the category O at positive rational levels, via a monoidal enhancement of Brundan and Stroppel’s semi-inifnite Ringel duality.
This is based on joint work with Johannes Flake and Robert McRae.