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On Poincaré–Birkhoff–Witt basis of the quantum general linear superalgebra

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Abstract

We give a detailed derivation of the commutation relations for the Poincaré–Birkhoff–Witt generators of the quantum superalgebra \(\mathrm U_q(\mathfrak{gl}_{M|N})\).

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Notes

  1. For the terminology used for integrability objects, we refer the reader to [6], [8], [11].

  2. See Appendix A of [22] for a minimal necessary set of definitions and notation.

  3. We note that if we define an ordering of positive roots such that \(\alpha_{i j} \prec \alpha_{m n}\) if \((i, j) \prec (m, n)\), we obtain a normal ordering in the sense of [24], [25] (also see [26]).

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Funding

This work was supported in part by the Russian Foundation for Basic Research (grant No. 20-51-12005).

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  1. Logunov Institute for High Energy Physics, National Research Center “Kurchatov Institute”, Protvino, Moscow Region, Russia

    A. V. Razumov

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  1. A. V. Razumov
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Correspondence to A. V. Razumov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 217, pp. 613–629 https://doi.org/10.4213/tmf10444.

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Razumov, A.V. On Poincaré–Birkhoff–Witt basis of the quantum general linear superalgebra. Theor Math Phys 217, 1938–1953 (2023). https://doi.org/10.1134/S0040577923120115

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