1995/06/30 by W. Rühl, Werner Ruhl, Alexander V. Turbiner +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #cond-mat #funct-an #hep-th #math.FA #nlin.SI #solv-int
paper · pdf · doi:10.1142/s0217732395002374
published as Mod. Phys. Lett. A10 (1995) 2213 · 13 pages, latex. Connection to Jack polynomials clarified, misprints corrected
arxiv created 1995/08/03 · openalex publication_date 1995/09/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Translationally invariant symmetric polynomials as coordinates for N-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland N-body Hamiltonians, after appropriate gauge transformations, can be presented as a quadratic polynomial in the generators of the algebra sl N in finitedimensional degenerate representation. The exact solvability of these models follows from the existence of the infinite flag of such representation spaces, preserved by the above Hamiltonians. A connection with Jack polynomials is discussed.