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
