Light-cone decomposition of a massive spin-two field (${\mathrm{Sym}}_0^2({\mathbb{R}}^{D-1})\downarrow SO(D-2)={\mathrm{Sym}}_0^2({\mathbb{R}}^{D-2})\oplus {\mathbb{R}}^{D-2}\oplus \mathbb{R}$)

When ${\partial }_{-}$ is invertible, divergence determines components with a plus index from $h_{--},h_{-I},h_{IJ}$. The trace constraint fixes the trace of $h_{IJ}$. The remaining transverse group representations are a symmetric traceless square, a vector representation, and a scalar.