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 $W^k(\lambda ,\mu )$ parameterized by partitions $\lambda$ and $\mu$ associated with the centralizers of nilpotent elements in ${\mathfrak{gl}}_N$. The…