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 $Z[\tilde{W}]$ of the extended affine Weyl group of $\widehat{sl}(3{)}_k$ at $k\notin Q$. 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 $\widehat{sl}(3{)}_k$.

contains two TeX files: main file using harvmac.tex, amssym.def, amssym.tex, 35p.; file with figures using XY-pic package, 4p; v2: minor corrections, Note added

Cited by in corpus (3)

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• Characters of $\widehat{sl}(4{)}_k$ fusion algebra at non-rational level