Наоки Генра: Screening operators for W-algebras and Wakimoto representations

The W-algebras are the families of vertex algebras associated with simple Lie (super)algebras and their nilpotent elements, defined as the associated quantized Drinfeld-Sokolov reduction. By a result of Feigin and Frenkel, the W-algebras associated with principal nilpotents may be described as the kernels of screening operators, called free fields realizations. I show the descriptions of the W-algebras for any Lie (super)algebras and nilpotents by using (generalized) screening operators (the direct generalizations of results of Feigin-Frenkel), and also give more explicit formulae of screening operators via Wakimoto representations for affine vertex algebras.