Wakimoto representations for $mathcal{W}$-algebras (Representation Theory and Related Areas)

Abstract

The mathcal{W}-algebras are vertex algebras defined by the generalized Drinfeld-Sokolov reductions. Using the Wakimoto reprcsentations of affine Lie algcbras, wc describe the explicit formulae of the screening operators for the mathcal{W}-algebras with generic level. As applications, we show that, the mathcal{W}-algebras of type A have the "coproduct" structures.