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

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

1998-07-20

arxiv.org/abs/math/9807106v2

Commun.Math.Phys. 202 (1999) 701-733

Mathematics

Quantum Algebra

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

Scientific paper

10.1007/s002200050602

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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