Geodesic
Affine super-Yangian and a~quantum Weyl groupoid
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 3, pp. 476-489

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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.
Keywords: Yangian for an affine Kac–Moody superalgebra, Kac–Moody Lie superalgebra.
Mots-clés : quantum Weyl group, Weyl groupoid 
@article{TMF_2023_216_3_a7,
     author = {V. D. Volkov and V. A. Stukopin},
     title = {Affine {super-Yangian} and a~quantum {Weyl} groupoid},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {476--489},
     publisher = {mathdoc},
     volume = {216},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a7/}
}
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V. D. Volkov; V. A. Stukopin. Affine super-Yangian and a~quantum Weyl groupoid. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 3, pp. 476-489. http://geodesic.mathdoc.fr/item/TMF_2023_216_3_a7/