Neveu–Schwarz level-one massive tensor (${\Lambda }^2({\mathbb{R}}^{D-1})\downarrow SO(D-2)={\Lambda }^2({\mathbb{R}}^{D-2})\oplus {\mathbb{R}}^{D-2}$)

The unprojected level-one states form a transverse vector representation and an exterior square. Fermionic anticommutation makes the two-fermion states antisymmetric. Together they restrict from an antisymmetric rank-two tensor of $SO(D-1)$, not a massive spin-two field.