On the Relation Between U q (sl(2)) Vertex Operators and q-Zonal Functions

We show how the states constructed from the action of the modes of bosonized vertex operators that intertwine U modules are related toq -zonal functions.     

Bosonized Wakimoto Construction in the Principal Gradation

It is well known that the bosonized version of the Wakimoto construction allows the explicit realization of any affine algebra , with arbitrary level k in the homogeneous gradation, in terms of dim free bosonic fields.However, its extension in the principal gradation has been achieved only in the simplest case k=1. In this Letter we show, in the case of the simplest affine algebra ,that the bosonized Wakimoto realization can be extended to the principal gradation only when k is equal to the critical level, i.e., –2.In this case, this construction can be achieved in terms ofarbitrary number (larger than 1) of free bosonic fields.