Representations of $U_{\epsilon}^{res}(sl_2)$ via Restricted q-Fock Spaces

Abstract

Two restricted $C[q,q^{-1}]-$forms of the well known q-boson algebra are introduced and the corresponding restricted q-Fock spaces defined. All of the irreducible highest weight representations, including the infinite dimensional ones, of $U_\epsilon ^{res}(sl_2)$ of type 1 are constructed through the restricted q-Fock spaces.