Cosets of Bershadsky-Polyakov algebras and rational $\mathcal{W}$-algebras of type $A$

Tomoyuki Arakawa, Thomas Creutzig, Andrew R. Linshaw

The Bershadsky-Polyakov algebra is the $\mathcal{W}$-algebra associated to $\mathfrak{s}{\mathfrak{l}}_3$ with its minimal nilpotent element $f_{\theta }$. For notational convenience we defi…