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A note on decoupling conditions for generic level $\hat{sl}(3)_k$ and fusion rules

A. Ch. Ganchev·V. B. Petkova·G. M. T. Watts
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Abstract

We find the solution of the $\hat{sl}(3)_k$ singular vector decoupling equations on 3-point functions for the particular case when one of the fields is of weight $w_0\cdot kΛ_0$. The result is a function with non-trivial singularities in the flag variables, namely a linear combination of 2F1 hypergeometric functions. This calculation fills in a gap in [1] and confirms the $\hat{sl}(3)_k$ fusion rules determined there both for generic $κ\not \in \IQ$ and fractional levels. We have also analysed the fusion in $\hat{sl}(3)_k$ using algebraic methods generalising those of Feigin and Fuchs and again find agreement with [1]. In the process we clarify some details of previous treatments of the fusion of $\hat{sl}(2)_k$ fractional level admissible representations.

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A. Ch. Ganchev, V. B. Petkova, G. M. T. Watts. 1999-06-17. A note on decoupling conditions for generic level $\hat{sl}(3)_k$ and fusion rules. https://doi.org/10.1016/s0550-3213(99)00745-2

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