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 $\mathfrak{g}$.

31 pages. latex file, minor revision, to appear in Communications in Contemporary Mathematics

References in corpus (2)

• Coproduct for the Yangian of an affine Kac-Moody algebra
• Equivalences between three presentations of orthogonal and symplectic Yangians