Yangians versus minimal W-algebras: A surprising coincidence

Abstract

We prove that the singularities of the [Formula: see text]-matrix [Formula: see text] of the minimal quantization of the adjoint representation of the Yangian [Formula: see text] of a finite dimensional simple Lie algebra [Formula: see text] are the opposite of the roots of the monic polynomial [Formula: see text] entering in the OPE expansions of quantum fields of conformal weight [Formula: see text] of the universal minimal affine [Formula: see text]-algebra at level [Formula: see text] attached to [Formula: see text].