An Explicit Construction of the Metaplectic Representation over a Finite Field

Markus Neuhauser

Abstract: This paper deals with the metaplectic representation of ${\rm Sp}(n,K)$, where $K$ is a finite field. We give an explicit, elementary and largely self-contained construction of the metaplectic representation over finite fields of characteristic $\neq 2$. The important steps of the construction will be given for a system of generating elements of ${\rm Sp}(n,K)$.

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