EVENT DETAILS AND ABSTRACT

Title: Flat Connections, braid groups and quantum groups
Speaker: Professor V. Toledano Laredo
Speaker Info: Univ. Paris VI
Brief Description:
Special Note:
Abstract:

I will review the construction of a flat connection D on the Cartan subalgebra of a complex, simple Lie algebra g with simple poles on the root hyperplanes and values in any finite-dimensional g-module. This connection, which was obtained in joint work with J. Millson, may be viewed as a generalisation of the Knizhnik-Zamolodchikov connection to the case of configuration spaces of other Lie types.

I will then explain how the work of Drinfeld and Kohno on the monodromy of the KZ connection leads one to conjecture that the monodromy of D is described by Lusztig's quantum Weyl group operators and will outline the recent proof of this conjecture.

references :

[1] V. Toledano Laredo, Quasi-Coxeter Algebras, Dynkin diagram cohomology and quantum Weyl groups, in preparation.

[2] J. J. Millson, V. Toledano-Laredo, Casimir Operators and Monodromy Representations of Generalised Braid Groups, to appear in Transform. Groups, math.QA/0405062

[3] V. Toledano Laredo, Flat Connections and Quantum Groups, Acta Appl. Math. 73 (2002), 155-173.

[4] V. Toledano Laredo, A Kohno-Drinfeld theorem for quantum Weyl groups. Duke Math. J. 112 (2002), 421-451.