2025/11/04 by Lin, Hongda, Zhang, Honglian
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2511.02393
In this paper, we investigate finite-dimensional irreducible representations of the quantum affine general linear superalgebra Uq(\widehat\mathfrakglm|n,s) for arbitrary 01-sequences s, using the RTT presentation. We systematically construct the RTT presentation for quantum general linear superalgebra Uq(\mathfrakglm|n,s), and derive a PBW basis induced by the action of the braid group, compatible with non-standard parities. We determine the necessary and sufficient conditions for the finite-dimensionality of irreducible representations of Uq(\mathfrakglm|n,s) and extend the results to the affine case via the evaluation homomorphism. Specific cases such as (m,n)=(1,1) demonstrate that all finite-dimensional representations are tensor products of typical evaluation representations. This work extends existing representation frameworks and classification methods to encompass arbitrary 01-sequences, establishing the foundation for subsequent research on representations of quantum affine superalgebras.