Yangians vs minimal W-algebras: a surprizing coincidence

TL;DR

This paper reveals a surprising coincidence between the singularities of the R-matrix in Yangian quantum groups and the roots of polynomials in W-algebras, connecting two areas of mathematical physics.

Contribution

It establishes a novel link between the singularities of the R-matrix in Yangians and the roots of polynomials in minimal affine W-algebras, showing a deep structural coincidence.

Findings

Singularities of R-matrix are opposite to roots of polynomial p(k).

Connection between Yangian R-matrix and W-algebra OPE expansions.

Provides new insights into the structure of quantum groups and W-algebras.

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 $\mathfrak g$.