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

TL;DR

This paper derives the BC(n) Sutherland Hamiltonian with arbitrary coupling constants through quantum Hamiltonian reduction of the Laplace operator on U(N), exploring three different reduction schemes.

Contribution

It introduces new reduction methods for deriving the BC(n) Sutherland model from the Laplacian on U(N), generalizing previous results.

Findings

Derived the BC(n) Sutherland Hamiltonian with arbitrary couplings.

Connected reduction schemes to previous work on complex BC(n) models.

Provided a unified framework for Hamiltonian derivations via group reductions.

Abstract

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.