2024/07/02 by Matheus Brito, Brito, Matheus, Marcelo De Martino +1
Mathematics · Physics and Astronomy · #05E10 #17B37 #20G42 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2407.02205
openalex publication_date 2024/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a quantum analogue of the classical metaplectic Howe duality involving the pair of Lie algebras (\mathfraksp2n,\mathfraksl2) in the case when n=1. Our results yield commuting representations of the pair of Drinfeld-Jimbo quantum groups (\mathcal Uq2(\mathfraksl2),\mathcal Uq(\mathfraksl2)) realized in a suitable algebra of q-differential operators acting on the space of symplectic polynomial spinors. We obtain q-analogues for the symplectic Dirac operator, the Fischer decomposition, the expression for the symplectic polynomial monogenics and for the projection operators onto the monogenics. We also discuss q-analogues of generalized symmetries of the q-symplectic Dirac operator raising the homogeneous polynomial degree.