Description
The KZ equations first arose in 2d conformal field theory, as constraints satisfied by correlation functions in the Wess--Zumino--Novikov--Witten model. The standard mathematical construction of the linear PDEs involves spaces of (co)vacua associated to highest-weight modules for affine Lie algebras, and a different derivation was later given by Reshetikhin and Harnad via quantisation of the Schlesinger Hamiltonians; in turn, the latter control isomonodromic deformations of Fuchsian systems on the Riemann sphere.
In this talk we will aim at a review of part of this story. If time allows we will also present a generalisation involving moduli spaces of (nongeneric) irregular singular connections, as well as `generalised' highest-weight modules for affine Lie algebras.
(This extension is joint work with P. Boalch, J. Douçot, G. Felder, M. Tamiozzo and R. Wentworth.)
