Modular representations arising from self-dual $\ell$-adic representations of finite groups

arXivmath/9809107MaRDI QIDQ6501019

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Abstract: Suppose $ell$ is a prime number, ${mathbfQ}_{e}ll$ is the field of $ell$-adic numbers, ${mathbfF}_{e}ll$ is the finite field of $ell$ elements, and $d$ is a positive integer. Suppose $G$ is a finite subgroup of a symplectic group $S{p}_{2d}({mathbfQ}_{e}ll)$. We prove that $G$ can be embedded in $S{p}_{2d}({mathbfF}_{e}ll)$ in such a way that the characteristic polynomials are preserved (mod $ell$), as long as $ell>3$.

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