1 Free boson representation of DY h̄ ( ̂ sl ( M + 1 | N + 1 ) ) at level one

ar X iv : h ep - t h / 97 09 01 6 v 1 2 S ep 1 99 7 Free boson representation of DY h̄ ( gl N ) k

Free Boson Representation of U q ( ŝl 2 )

A representation of the quantum affine algebra U q (ˆ sl 2) of an arbitrary level k is realized in terms of three boson fields, whose q → 1 limit becomes the Wakimoto representation. An analogue of the screening current is also obtained. It commutes with the action of U q (ˆ sl 2) modulo total difference of some fields.

q-AFFINE-YANGIAN DOUBLE CORRESPONDENCE AND FREE BOSON REPRESENTATION OF YANGIAN DOUBLE WITH ARBITRARY LEVEL

We derive a free boson representation of the Yangian double DY~(slN ) 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. Date: January 1997. 0 FREE BOSON REPRESENTATION OF YANGIAN DOUBLE 1

un 1 99 6 A LEVEL - ONE REPRESENTATION OF THE QUANTUM

A level-one representation of the quantum affine superalgebra U q (sl(M + 1|N + 1)) and vertex operators associated with the fundamental representations are constructed in terms of free bosonic fields. Character formulas of level-one irreducible highest weight modules of U q (sl(2|1)) are conjectured.

A Level - One Representation of the Quantum

A level-one representation of the quantum affine superalgebra U q (sl(M + 1|N + 1)) and vertex operators associated with the fundamental representations are constructed in terms of free bosonic fields. Character formulas of level-one irreducible highest weight modules of U q (sl(2|1)) are conjectured.