Twisted spin Sutherland models from quantum Hamiltonian reduction

Abstract

Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems associated with arbitrary finite dimensional irreducible representations of the group by using the symmetry induced by twisted conjugations are described in detail. These systems generically yield integrable Sutherland type many-body models with spin, which are called twisted spin Sutherland models if the underlying twisted conjugations are built on non-trivial Dynkin diagram automorphisms. The spectra of these models can be calculated, in principle, by solving certain Clebsch-Gordan problems, and the result is presented for the models associated with the symmetric tensorial powers of the defining representation of SU(N).

30 pages

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Cited by in corpus (8)

• Poisson-Lie analogues of spin Sutherland models
• Degenerate integrability of quantum spin Calogero--Moser systems
• Hamiltonian reductions of free particles under polar actions of compact Lie groups
• Poisson reductions of master integrable systems on doubles of compact Lie groups
• Generalized spin Sutherland systems revisited
• Introduction to Lie groups, isometric and adjoint actions and some generalizations
• Poisson-Lie analogues of spin Sutherland models revisited
• Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems and KZB equations