Derivations of the trigonometric BC(n) Sutherland model by quantum Hamiltonian reduction

Details Derivations of the trigonometric BC(n) Sutherland model by quantum Hamiltonian reduction Derivations of the trigonometric BC(n) Sutherland model by quantum Hamiltonian reduction

2009-09-28

arxiv.org/abs/0909.5208v2

Rev.Math.Phys.22:699-732,2010

Physics

Mathematical Physics

30 pages, LateX; v2: final version with minor stylistic modifications

Scientific paper

10.1142/S0129055X10004065

The BC(n) Sutherland Hamiltonian with coupling constants parametrized by three arbitrary integers is derived by reductions of the Laplace operator of the group U(N). The reductions are obtained by applying the Laplace operator on spaces of certain vector valued functions equivariant under suitable symmetric subgroups of U(N)\times U(N). Three different reduction schemes are considered, the simplest one being the compact real form of the reduction of the Laplacian of GL(2n,C) to the complex BC(n) Sutherland Hamiltonian previously studied by Oblomkov.

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