2024/10/29 by Xianghua Wu, Wu, Xianghua, Hongda Lin +3 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2410.21755
In this paper, we investigate the structure of the quantum affine superalgebra associated with the orthosymplectic Lie superalgebra \mathfrakosp(2m+1|2n) for m\geqslant 1. The Drinfeld-Jimbo presentation for this algebra, denoted as Uq[\mathfrakosp(2m+1|2n)(1)], was originally introduced by H. Yamane. We provide the definition of the Drinfeld presentation Uq[\mathfrakosp(2m+1|2n)(1)]. To establish the isomorphism between the Drinfeld-Jimbo presentation and the Drinfeld presentation of the quantum affine superalgebra for type \mathfrakosp(2m+1|2n), we introduce a braid group action to define quantum root vectors of the quantum superalgebra. Specifically, we present an efficient method for verifying the isomorphism between two presentations of the quantum affine superalgebra associated with the type \mathfrakosp(2m+1|2n).