Electronic states of VO vanadium oxide in $C_{2v}$ point group

The electron configuration of $V^{2+}$: ... 3$d^{3}$ with 3 d electrons in 3 d orbitals. In $C\_{\infty v}$, $d\_{xz}$ and $d\_{yz}$ have $\Pi$ IRREP; $d\_{z}^{2}$ has $\Sigma^{+}$ IRREP; $d\_{x^{2}-y^{2}}$ and $d\_{xy}$ have $\Delta$ IRREP. So I think the 3 lowest lying orbitals are $\Sigma^{+}$ and $\Pi$. The 2 possible spins are doublet and quartet. The 3 spatial occupations are


1. $\Sigma^{+}$ x $\Pi$ x $\Pi$ = $\Sigma^{+}$ + [$\Sigma^{-}$] + $\Delta$
2. $\Sigma^{+}$ x $\Sigma^{+}$ x $\Pi$ = $\Pi$
3. $\Pi$ x $\Pi$ x $\Pi$ = ($\Sigma^{+}$ + [$\Sigma^{-}$] + $\Delta$) x $\Pi$ = $\Pi$ + $\Pi$ + $\Pi$ + $\Phi$


I only know that $\Sigma^{+}$ is symmetric and $\Sigma^{-}$ is antisymmetric. But I'm not sure about other IRREPs' symmetry ($\Pi$, $\Delta$, $\Phi$). Also I don't know how the sum of many IRREPs which should also takes into account the various occupation permutations is transformed into $C\_{2v}$. And since the $O^{2-}$ is fully occupied, only $V^{2+}$ contributes to the MOs. (Or is the concept of MO invalid in ionic bonding?) Is that correct?


Also a book recommendation for group theory in transition metal complex would be very much appreciated.


