A lecture on the Calogero-Sutherland models

Abstract

In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shastry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor of the density operator. 2) The Dunkl operators and their relations with monodromy matrices, Yangians and affine-Hecke algebras. 3) The Haldane-Shastry chain in connection with the Calogero-Sutherland Hamiltonian at a specific coupling constant.

(2 references added, small modifications)

References in corpus (2)

• Exchange Operator Formalism for Integrable Systems of Particles
• Yang-Baxter equation in spin chains with long range interactions

Cited by in corpus (5)

• Quantum Elliptic Calogero-Moser Systems from Gauge Origami
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains
• Finite-Range Coulomb Gas Models I: Some Analytical Results
• Scattering matrices and affine Hecke algebras