  In this work we review the derivation of Dirac and Weinberg equations based
on a ``principle of indistinguishability'' for the (j,0) and (0,j) irreducible
representations (irreps) of the Homogeneous Lorentz Group (HLG). We generalize
this principle and explore its consequences for other irreps containing spin >=
1. We rederive Ahluwalia-Kirchbach equation using this principle and conclude
that it yields O(p^{2j}) equations of motion for any representation containing
spin j and lower spins. We also use the obtained generators of the HLG for a
given representation to explore the possibility of the existence of first order
equations for that representation. We show that, except for j=1/2, there exists
no Dirac-like equation for the (j,0)\oplus (0,j) representation nor for the
(1/2,1/2) representation. We rederive Kemmer-Duffin-Petieau (KDP) equation for
the (1,0)\oplus (1/2,1/2)\oplus(0,1) representation by this method and show
that the (1,1/2)\oplus (1/2,1) representation satisfies a Dirac-like equation
which describes a multiplet of j=3/2 and j=1/2 with masses m and m/2}
respectively.
