University of Toronto's Symplectic Geometry Seminar

November 12, 2007, 2:10pm

Bahen 6183

Valerio Toledano Laredo

IAS and Northeastern University

Gaudin models with irregular singularities.


The Casimir connection of a simple Lie algebra g yields a family of commuting quantum Hamiltonians acting on the weight spaces of g-modules. I will explain how to diagonalise these Hamiltonians by using the affine Kac--Moody algebra \hat{g} at critical level. This mirrors the construction of Feigin--Frenkel--Reshetikhin, who diagonalised the Gaudin Hamiltonians arising from the Knizhnik--Zamolodchikov connection, and leads to a new class of quantum integrable systems generalizing the Gaudin model. These integrable systems are quantisations of the shift of argument algebras, that is the maximal Poisson commutative subalgebras of Sg introduced by Mishenko--Fomenko.

This is joint work with B. Feigin and E. Frenkel.