Affine super-Yangian and a quantum Weyl groupoid

V. D. Volkov   ; V. A. Stukopin

Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 3, pp. 476-489

Résumé

We define two realizations of the affine super-Yangian $Y_{\hbar}(\widehat{sl}(m|n))$ for a special linear Kac–Moody superalgebra $\widehat{sl}(m|n)$ and an arbitrary system of simple roots: in terms of a “minimalist” system of generators and in terms of the new system of Drinfeld generators. We construct an isomorphism between these two realizations of the super-Yangian in the case of a fixed system of simple roots. We consider the Weyl groupoid, define its quantum analogue, and its action on the super Yangians defined by the systems of simple roots. We show that the action of the quantum Weyl groupoid induces isomorphisms between super-Yangians defined by different simple root systems.

Détail

Keywords: Yangian for an affine Kac–Moody superalgebra, quantum Weyl group, Kac–Moody Lie superalgebra.
Mots-clés : Weyl groupoid

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