Derivation of Green's function of a spin Calogero-Sutherland model by Uglov's method

The hole propagator of a spin 1/2 Calogero-Sutherland model is derived using Uglov's method, which maps the exact eigenfunctions of the model, called the Yangian Gelfand-Zetlin basis, to a limit of Macdonald polynomials (gl2-Jack polynomials). To apply this mapping method to the calculation of 1-particle Green's function, we confirm that the sum of the field annihilation operator ψu + ψ↓ on a Yangian Gelfand-Zetlin basis is transformed to the field annihilation operator ψ on gl2-Jack polynomials by the mapping. The resultant expression for the hole propagator for a finite-size system is written in terms of renormalized momenta and spin of quasi-holes, and the expression in the thermodynamic limit coincides with the earlier result derived by another method. We also discuss the singularity of the spectral function for a specific coupling parameter where the hole propagator of the spin Calogero-Sutherland model becomes equivalent to the dynamical colour correlation function of an SU(3) Haldane-Shastry model