1994/11/30 by Hidetoshi Awata, H. Awata, Y. Matsuo +5
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Combinatorics #Eigenvalues and eigenvectors #Field (mathematics) #Graph #Hamiltonian (control theory) #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Vertex (graph theory) #cond-mat #hep-th
paper · pdf · doi:10.1016/0370-2693(95)00055-p
published as Phys. Lett. B347 (1995) 49 · 13 pages, latex, no figures, a few references added
arxiv created 1994/12/12 · openalex publication_date 1995/03/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
On the basis of the collective field method, we analyze the Calogero--Sutherland model (CSM) and the Selberg--Aomoto integral, which defines, in particular case, the partition function of the matrix models. Vertex operator realizations for some of the eigenstates (the Jack polynomials) of the CSM Hamiltonian are obtained. We derive Virasoro constraint for the generalized matrix models and indicate relations with the CSM operators. Similar results are presented for the q--deformed case (the Macdonald operator and polynomials), which gives the generating functional of infinitely many conserved charges in the CSM.