Carissimi,

vi ricordo il prossimo Seminario di Algebra, Topologia e Combinatoria, che si terrà venerdì:

The Casimir connection of a Kac-Moody algebra Andrea Appel University of Southern California venerdì 18 dicembre, 16:00 Sala Riunioni

Abstract: I will first introduce the Casimir connection of a symmetrizable Kac–Moody algebra g. This is a flat connection over the Cartan subalgebra of g, with values in Ug and logarithmic singularities on the root hyperplanes. It is equivariant with respect to the action of the Weyl group, and its monodromy gives rise to a representation of the generalised braid group of type g (in particular, this includes affine braid groups).

I will then give a brief overview of the description of this monodromy representation in terms of the quantum Weyl group operators of the quantum group Uh(g). The proof relies on the notion of quasi–Coxeter category, which is to a generalised braid group what a braided monoidal category is to the standard braid group on n strands. In particular, the result follows from the construction of an equivalence of quasi–Coxeter categories between the integrable highest weight representations of Ug and those of Uh(g). This is joint work with V. Toledano Laredo.

Un saluto,

Filippo