q-affine-Yangian double correspondence and free boson representation of Yangian double with arbitrary level

Abstract

We derive a free boson representation of the Yangian double $DY_\hbar(sl_N)$ with arbitrary level k using the observation that there is a correspondence between the q-affine algebra and Yangian double associated with the same Cartan matrix. Vertex operator and screening currents are not obtained in the same way.

LaTeX file, amssymb and amsart used. 13 pages, no figures. Several misprints corrected, some in important formulas