and (\[irr\]) has nontrivial solutions only for the choice of the unitary infinite-dimensional representations of the discrete type series $D^\pm_{\alpha}$, whereas for $\alpha=-j<0$, $j$ being integer or half-integer, nontrivial solutions take place only under the choice of the $(2j+1)$-dimensional nonunitary representations $\tilde{D}{}_j$ of the group $\overline{\rm SL(2,R)}$. Such $(2j+1)$-dimensional nonunitary representations are related to the corresponding unitary representations $D_j$ of the group $SU(2)$, and, in particular, in the simplest cases $j=1/2$ and $j=1$ they describe the spinor and vector representations of the (2+1)-dimensional Lorentz group [@cor]. In these two cases eqs. (\[vector\]) can be reduced to the Dirac and to the Jackiw-Temleton-Schonfeld equations, respectively. As soon as the representation is chosen (and, so, eq. (\[irr\]) is satisfied identically), the following identity takes place for the vector differential operatorR$\ $R$V_\mu$: $$\begin{aligned}
&R^\mu V_\mu \equiv 0,&
\nonumber\\
&R_\mu= \left( (\alpha-1)^2 \eta_{\mu\nu} -
i(\alpha-1)\epsilon_{\mu\nu\lambda} J^{\lambda}
+J_{\nu} J_{\mu} \right)P^\nu.&
\nonumber\end{aligned}$$ This identity means that after fixing a choice of an admissible representation, three equations (\[vector\]) become to be dependent ones, and in general case any two of them are independent (in the above mentioned cases of the finite dimensional nonunitary spinor and vector representations, eqs. (\[vector\]) contain only one independent equation). Therefore, the total 