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

P. Furlan·A. Ch. Ganchev·V. B. Petkova
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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 $\hat{sl}(3)_k$ at $k\not \in Q$. 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 $\hat{sl}(3)_k$.

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P. Furlan, A. Ch. Ganchev, V. B. Petkova. 1998-11-26. An Extension of the Character Ring of sl(3) and Its Quantisation. https://doi.org/10.1007/s002200050602

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