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

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.

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

References in corpus (3)

• Physics and Mathematics of Calogero particles
• A class of Calogero type reductions of free motion on a simple Lie group
• Hamiltonian reductions of free particles under polar actions of compact Lie groups

Cited by in corpus (8)

• Superintegrability of $d$-dimensional Conformal Blocks
• Harmony of Spinning Conformal Blocks
• From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models
• Calogero-Sutherland Approach to Defect Blocks
• N-point spherical functions and asymptotic boundary KZB equations
• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• An integrable BC(n) Sutherland model with two types of particles