Generalizations of spin Sutherland models from Hamiltonian reductions of Heisenberg doubles

Speaker

My area of interest is mathematical physics in general, especially the theory of integrable Hamiltonian systems. I often apply Lie group theoretic methods in my investigations. After studies of Kepler-like systems and Berry’s phase, my research focused on models of conformal field theory and their symmetry algebras, then on soliton equations, dynamical Yang-Baxter structures and action–angle dualities of Calogero–Moser type many-body models. With collab- orators, up to now I published around 90 research papers in refereed journals and around 20 papers in refereed conference proceedings. I presented talks on my results at about 75 inter- national conferences. My papers received nearly 2000 independent citations.

Abstract

The talk is devoted to generalizations of classical spin Sutherland models. The models of interest result from reductions of master integrable systems defined on the Heisenberg doubles of compact Lie groups. The unreduced systems are natural Poisson–Lie symmetric counterparts of the Hamiltonian systems of free motion living on the cotangent bundles T∗G. We take an arbitrary connected and simply connected compact Lie group G and analyze the reduced system that descends to the Poisson quotient of the Heisenberg double via an analogue of the conjugation action of G on T∗G. In particular, we explain that the reduced systems possess the property of degenerate integrability on the dense open subset of the Poisson quotient space corresponding to the principal orbit type for the group action, and describe their connection with the spin Sutherland models.