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On sl3 Knizhnik-Zamolodchikov equations and W3 null-vector equations
Sylvain Ribault1

Starting from Sklyanin's separation of variables for the sl3 Yangian model, we derive the separation of variables for the quantum sl3 Gaudin model. We use the resulting new variables for rewriting the sl3 Knizhnik-Zamolodchikov equations, and comparing them with certain null-vector equations in conformal field theories with W3-algebra symmetry. The two sets of equations are remarkably similar, but become identical only in the critical level limit. This is in contrast to the sl2 Knizhnik-Zamolodchikov equations, which are known to be equivalent to Belavin-Polyakov-Zamolodchikov equations for all values of the level.
1 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
Physique/Physique des Hautes Energies - Théorie

Mathématiques/Physique mathématique
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