Affine symplectic group (awaiting review)

The affine symplectic group $\ASp(n,q)$ is the subgroup of the affine general linear group $\AGL(n,q) = \F_q^n \rtimes \GL(n,q)$ of all affine transformations $x \mapsto Mx + v$ such that $M$ is an element of the symplectic group $\Sp(n,q)$.