2023/09/27 by Güner Muarem, Muarem, Guner
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Atomic Physics (physics.atom-ph) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2309.15626
openalex publication_date 2023/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we will study both the finite and infinite-dimensional representations of the symplectic Lie algebra \mathfraksp(2n) and develop a polynomial model for these representations. This means that we will associate a certain space of homogeneous polynomials in a matrix variable, intersected with the kernel of \mathfraksp(2n)-invariant differential operators related to the symplectic Dirac operator with every irreducible representation of \mathfraksp(2n). We will show that the systems of symplectic Dirac operators can be seen as generators of parafermion algebras. As an application of these new models, we construct a symplectic analogue of the Rarita-Schwinger operator using the theory of transvector algebras.