Poisson-Lie T duality and integrable systems

H. MONTANI

FAMAF, Córdoba

Congreso; Reunión Anual de Unión Matemática Argentina; 2007

Unión Matemática Argentina (UMA)

We describe a hamiltonian analysis of Poisson-Lie T-duality based on the geometry of the underlying phases spaces of the dual sigma and WZW models. Duality is fully characterized by the existence of a hamiltonian action of a Drinfeld double Lie group on the cotangent bundle of its factors and the associated equivariant momentum maps. The duality transformations are explicitly constructed in terms of these actions. It is shown that compatible integrable dynamics arise in a general collective form.