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arXiv · 2309.15626

Models for irreducible representations of the symplectic algebra using Dirac-type operators

Guner Muarem
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Abstract

In this paper we will study both the finite and infinite-dimensional representations of the symplectic Lie algebra $\mathfrak{sp}(2n)$ 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 $\mathfrak{sp}(2n)$-invariant differential operators related to the symplectic Dirac operator with every irreducible representation of $\mathfrak{sp}(2n)$. 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.

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Guner Muarem. 2023-09-27. Models for irreducible representations of the symplectic algebra using Dirac-type operators. https://arxiv.org/abs/2309.15626

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