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

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

1998-09-18

arxiv.org/abs/math/9809107v1

Mathematics

Group Theory

Scientific paper

Suppose $\ell$ is a prime number, ${\mathbf Q}_\ell$ is the field of $\ell$-adic numbers, ${\mathbf F}_\ell$ is the finite field of $\ell$ elements, and $d$ is a positive integer. Suppose $G$ is a finite subgroup of a symplectic group $Sp_{2d}({\mathbf Q}_\ell)$. We prove that $G$ can be embedded in $Sp_{2d}({\mathbf F}_\ell)$ in such a way that the characteristic polynomials are preserved (mod $\ell$), as long as $\ell>3$.

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