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Drinfeld Realization for Quantum Affine Orthosymplectic Superalgebras
[Submitted on 9 May 2024 (v1), last revised 23 Jun 2026 (this ve · 2026-06-24 · via math updates on arXiv.org

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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.

Submission history

From: Luan Bezerra [view email]
[v1] Thu, 9 May 2024 04:10:22 UTC (33 KB)
[v2] Tue, 23 Jun 2026 16:34:44 UTC (33 KB)

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