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Yangians versus minimal $W$ $W$ -algebras: A surprising coincidence

Victor G. Kac

Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

E-mail Address: kac@math.mit.edu

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Pierluigi Möseneder Frajria

Politecnico di Milano, Polo regionale di Como, Via Valleggio 11, 22100, Como, Italy

E-mail Address: pierluigi.moseneder@polimi.it

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Paolo Papi

Dipartimento di Matematica, Sapienza Università di Roma, P.le A. Moro 2, 00185, Roma, Italy

E-mail Address: papi@mat.uniroma1.it

Corresponding author.

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https://doi.org/10.1142/S0219199720500364Cited by:2 (Source: Crossref)

Abstract

We prove that the singularities of the $R$ $R$ -matrix $R (k)$ $R (k)$ of the minimal quantization of the adjoint representation of the Yangian $Y (𝔤)$ of a finite dimensional simple Lie algebra $𝔤$ 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 $𝔤$ .

Keywords:

AMSC: 17B37, 17B69

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