Colloquium

Spin Calogero-Sutherland type models from Hamiltonian reduction

Laszlo Feher

8月22日(水) 10時30分

We first survey general results on classical and quantum Hamiltonian reductions of the free geodesic motion on complete Riemannian manifolds under polar actions of compact symmetry groups, i.e., isometric actions that admit regularly embedded, closed, connected submanifolds meeting all orbits orthogonally in the configuration space. We thenexplain that if the original configuration space is a Lie group, or a symmetric space, and the orthogonal `section' of the orbits can be realized as a suitable Abelian subgroup, then the Hamiltonian reductions of the free particle typically yield spin Calogero-Sutherland type integrable models. We present several examples that fit in this framework, including the standard (spinless) BC(n) Sutherland models with three independent coupling constants.