Emmy-Noether-Seminar: Classical W-algebras via Adler-Gelfand-Dickey realization and Drinfeld-Sokolov reduction

Classical W-algebras via Adler-Gelfand-Dickey realization and Drinfeld-Sokolov reduction

Uhi Rinn Suh (Seoul)

Abstract: Adler and Gelfand–Dickey constructed integrable systems associated with the classical W_n-algebra using a scalar Lax operator of degree n. Later, Drinfeld Sokolov showed that the same structures can be obtained from an nxn linear Lax operator. The Drinfeld-Sokolov approach makes it possible to clearly observe the structure of the classical principal W-algebra for a general reductive Lie algebra and to derive the corresponding integrable systems. Subsequently, De Sole-Kac-Valeri combined the Adler-Gelfand-Dickey and Drinfeld-Sokolov methods to obtain results for arbitrary classical W-algebras. In this talk, I will explain how these methods can be extended to classical W-algebras or SUSY W-algebras.