Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model

Abstract

A zero modes' Fock space ℱq is constructed for the extended chiral su(2) WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping algebra U q=Uqsl(2) at an even root of unity, qh=-1, and of its infinite dimensional extension Ũq by the Lusztig operators E(h), F(h). We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations of Uq. A central result is the characterization of the Grothendieck ring of both Uq and Ũq in Theorem 3.1. The properties of the Ũq fusion ring in ℱq are related to the braiding properties of correlation functions of primary fields of the conformal sû(2)h-2 current algebra model. © 2007 Springer.