Yangians vs minimal W-algebras: a surprizing coincidence

Abstract

We prove that the singularities of the $R$-matrix $R(k)$ of the minimal quantization of the adjoint representation of the Yangian $Y(\mathfrak g)$ of a finite dimensional simple Lie algebra $\mathfrak g$ are the opposite of the roots of the monic polynomial $p(k)$ entering in the OPE expansions of quantum fields of conformal weight $3/2$ of the universal minimal affine $W$-algebra at level $k$ attached to $\mathfrak g$.