IntegrableN-particle Hamiltonians with Yangian or reflection algebra symmetry

2003/10/31 by V. Caudrelier, V Caudrelier, N. Crampe +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #math.QA #msc:70H06 #msc:81R12 #msc:81R50

paper · pdf · doi:10.1088/0305-4470/37/24/007

published as J.Phys.A37:6285-6298,2004 · 17 pages. Some typos corrected, references added and proofs clarified

openalex publication_date 2004/06/03 · arxiv created 2004/06/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We use the Dunkl operator approach to construct one-dimensional integrable models describing N particles with internal degrees of freedom. These models are described by a general Hamiltonian belonging to the centre of the Yangian or the reflection algebra, which ensures that they admit the corresponding symmetry. In particular, the open problem of the symmetry is answered for the B N -type Sutherland model with spin and for a generalized B N -type nonlinear Schrödinger Hamiltonian.

Citations

• Explicit Solution to the N-Body Calogero Problem
• Differential-difference operators associated to reflection groups
• Boundary conditions for integrable quantum systems

Cited by

• Sutherland models for complex reflection groups