The orthogonal eigenbasis and norms of eigenvectors in the Spin Calogero-Sutherland Model

Abstract

Using a technique based on the Yangian Gelfand-Zetlin algebra and the associated Yangian Gelfand-Zetlin bases we construct an orthogonal basis of eigenvectors in the Calogero-Sutherland Model with spin, and derive product-type formulas for norms of these eigenvectors.

35 pages, AMSLaTeX

References in corpus (10)

• Yang-Baxter equation in spin chains with long range interactions
• Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
• Quantum $W_N$ Algebras and Macdonald Polynomials
• Fractional Statistics in One-Dimension: View From An Exactly Solvable Model
• Dynamical correlation functions in the Calogero-Sutherland model
• Interacting Fermion Systems from Two Dimensional QCD
• Density Correlation Functions in Calogero Sutherland Models
• Exact Solution of the Sutherland Model with arbitrary symmetry
• Global fluctuation formulas and universal correlations for random matrices and log-gas systems at infinite density
• Jack polynomials and the multi-component Calogero-Sutherland model

Cited by in corpus (18)

• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Finite-dimensional irreducible representations of twisted Yangians
• Electron Addition Spectrum in the Supersymmetric t-J Model with Inverse-Square Interaction
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• Exact dynamical structure factor of the degenerate Haldane-Shastry model
• Exact Dynamics of the SU(K) Haldane-Shastry Model
• Spin-Ruijsenaars, q-deformed Haldane-Shastry and Macdonald polynomials
• Exact Charge Dynamics in the Supersymmetric t-J Model with Inverse-Square Interaction
• Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
• Exact spin dynamics of the 1/r^2 supersymmetric t-J model in a magnetic field
• Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial
• Dynamical correlation functions of the spin Calogero-Sutherland model
• The Yangian Symmetry in the Spin Calogero Model and its Applications
• From fermionic spin-Calogero-Sutherland models to the Haldane-Shastry chain by freezing
• Algebraic study on the $A_{N-1}$- and $B_N$-Calogero models with bosonic, fermionic and distinguishable particles
• Bethe ansatz inside Calogero-Sutherland models
• Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method
• Particle Propagator of Spin Calogero-Sutherland Model