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arXiv · 2405.05533

Drinfeld Realization for Quantum Affine Orthosymplectic Superalgebras

Luan Bezerra·Vyacheslav Futorny·Iryna Kashuba
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Abstract

A well-defined braid groupoid action is an essential tool for constructing the new Drinfeld realization of a quantum affine superalgebra. For quantum affine orthosymplectic superalgebras (types B, C, and D), this action was not fully defined, as the braid operators $T_i$ were known only up to normalization factors. In this paper, we solve this problem by providing the explicit formulas for these operators for any choice of parity. This yields a well-defined braid group action on the direct sum of these superalgebras. As a consequence, we use this action to formally introduce the new Drinfeld realization $U_q^D(\widehat{\mathfrak{g}}_s)$ for these types and prove that the corresponding Drinfeld-Jimbo quantum group $U_q(\widehat{\mathfrak{g}}_s)$ is its surjective homomorphic image. We conjecture that this map is an isomorphism.

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BibTeXRIS

Luan Bezerra, Vyacheslav Futorny, Iryna Kashuba. 2024-05-09. Drinfeld Realization for Quantum Affine Orthosymplectic Superalgebras. https://doi.org/10.1142/s021919972650063x

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