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.
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)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。