Explicit generators in rectangular affine \(\mathcal{W}\)-algebras of type \(A\)

Tomoyuki Arakawa and Alexander Molev

Abstract

We produce in an explicit form free generators of the affine \(\mathcal{W}\)-algebra of type \(A\) associated with a nilpotent matrix whose Jordan blocks are of the same size. This includes the principal nilpotent case and we thus recover the quantum Miura transformation of Fateev and Lukyanov.