  In this work, we systematically derive explicit expressions for the
Poincar\'e Group generators on arbitrary-rank tensors and spinor-tensors in
$D=3+1$ and $D=2+1$ spacetimes, thus generalizing previous works in the
literature for the groups $ISO(3,1)$ and $ISO(2,1)$. From the Casimir
eigenvalue equations, we demonstrate in a model-independent way the Fierz-Pauli
constraints for massive particles for spins $\mathfrak{s}=5/2$, 3, and 4 in
$D=3+1$ and helicities $\alpha=5/2$, 3, and 4 in $D=2+1$ dimensions. We also
comment on the demonstration of the Fierz-Pauli constraints for the general
case of arbitrary spin (helicity).
