Hello everybody!

Define the action of $SL_4({\mathbb{Z}})$ on alternating 2-forms or simply skew-symmetric matrices of degree 4 according to the following:

For $B \in SL_4({\mathbb{Z}})$ and an alternating matrix like $M$ define: $B.M = BMB^{T}$

Question: Why the single invariant for this action is $Pf(M)$?

Question2: Or why the invariant will be the coefficient of $Pf(Mx-Ny)$ by considering the action of $SL_4({\mathbb{Z}})$ on the pairs of skew-symmetric matrices instead?

Thanks ;)