Revista de la Unión Matemática Argentina
versión On-line ISSN 1669-9637
MONTANI, H.. Poisson-Lie T-duality and integrable systems. Rev. Unión Mat. Argent. [online]. 2008, vol.49, n.1, pp. 71-82. ISSN 1669-9637.
We describe a hamiltonian approach to 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.