Generalized finite and affine $W$-algebras in type $A$

Dong Jun Choi, Alexander Molev, Uhi Rinn Suh

We construct a new family of affine $W$-algebras $W^k(\hat{I}»,\hat{I}¼)$ parameterized by partitions $\hat{I}»$ and $\hat{I}¼$ associated with the centralizers of nilpotent elements in ${\mathfrak{gl}}_N$.…