Yangian Gelfand—Zetlin Bases, glN-Jack Polynomials, and Computation of Dynamical Correlation Functions in the Spin Calogero—Sutherland Model

  • Denis Uglov
Part of the CRM Series in Mathematical Physics book series (CRM)


We consider the gl N -invariant Calogero—Sutherland models with N = 1, 2, 3, … in the framework of symmetric polynomials. The Hamiltonian of any such model admits a distinguished orthogonal eigenbasis characterized as the union of Yangian Gelfand—Zetlin bases of irreducible components with respect to the Yangian action on the space of states. We construct an isomorphism from the space of states into the space of symmetric Laurent polynomials that maps the eigenbasis into the basis of gl N - Jack polynomials. These polynomials are defined as specializations of Macdonald polynomials where both parameters approach an Nth primitive root of unity. As an application of this isomorphism we compute two-point dynamical spin-density and density correlation functions in the gl 2-invariant Calogero-Sutherland model at integer values of the coupling constant.


Symmetric Polynomial Laurent Polynomial Macdonald Polynomial Jack Polynomial Density Correlation Function 
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© Springer Science+Business Media New York 2000

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  • Denis Uglov

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