$W$-algebras arise naturally from Drinfeld–Sokolov reduction and have important connections to representation theory and integrable systems. In this talk, I will discuss classical affine $W$-algebras and their deformed counterparts in type $A$, focusing on their Poisson structures.

I will first give a brief overview of $W$-algebras and their connections to quantum affine algebras. I will then explain how deformed $W$-algebras can be constructed through a deformed Drinfeld–Sokolov reduction, and describe their generators, Poisson brackets, and Miura transformations. Finally, I will show how classical affine $W$-algebras and their Poisson structures can be recovered from the deformed $W$-algebras through a limiting process.

발표시간 : 16:00 ~ 17:00