Strong generators of the subregular W-algebra and combinatorial description at critical level

Abstract

We construct explicitly strong generators of the affine $\mathcal{W}$-algebra ${\mathcal{W}}^{K-N}({\mathfrak{sl}}_N,f_{sub})$ of subregular type $A$. Moreover, we are able to describe the OPEs between them at critical level. We also give a description the affine $\mathcal{W}$-algebra ${\mathcal{W}}^{-N}({\mathfrak{sl}}_N,f_{sub})$ in terms of certain fermionic fields, which was conjectured by Adamović.

16 pages