An Extension of the Character Ring of sl(3) and Its Quantisation

Abstract:

We construct a commutative ring with identity which extends the ring of characters of finite dimensional representations of sl(3). It is generated by characters with values in the group ring of the extended affine Weyl group of at . The “quantised” version at rational level k+3=3/p realises the fusion rules of a WZW conformal field theory based on admissible representations of .