### 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) × 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.

Original language | English |
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Pages (from-to) | 699-732 |

Number of pages | 34 |

Journal | Reviews in Mathematical Physics |

Volume | 22 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jul 1 2010 |

### Keywords

- Integrable many-body systems
- polar action
- quantum Hamiltonian reduction

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Fehér, L., & Pusztai, B. G. (2010). Derivations of the trigonometric BC

_{n}Sutherland model by quantum Hamiltonian reduction.*Reviews in Mathematical Physics*,*22*(6), 699-732. https://doi.org/10.1142/S0129055X10004065