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Affine super-Yangian and a quantum Weyl groupoid

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Abstract

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.

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Funding

The work was performed at the MIPT Center of Fundamental Mathematics under financial support of the state project (FSMG-2023-0013). This work was also supported by the Russian Science Foundation (grant No. 23-21-00282).

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), Center of Fundamental Mathematics, MIPT, Dolgoprudny, Moscow region, Russia

    V. D. Volkov & V. A. Stukopin

  2. South Mathematical Institute, Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, Russia

    V. A. Stukopin

  3. Moscow Center for Continuous Mathematical Education, Moscow, Russia

    V. A. Stukopin

Authors
  1. V. D. Volkov
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  2. V. A. Stukopin
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Correspondence to V. A. Stukopin.

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The authors declare no conflicts of interest.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 216, pp. 476–489 https://doi.org/10.4213/tmf10455.

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Volkov, V.D., Stukopin, V.A. Affine super-Yangian and a quantum Weyl groupoid. Theor Math Phys 216, 1313–1325 (2023). https://doi.org/10.1134/S0040577923090064

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