are defined by the relation of the form of eq. (\[apq\]) as linear hermitian combinations of $a^\pm$. In terms of the operators $L_\alpha$, $\alpha=1,2$, the corresponding part of the deformed Heisenberg algebra (\[hei\]) and (\[klein\]) is presented as $$[L_\alpha,L_\beta]=i\epsilon_{\alpha\beta}\cdot(1+\nu K),\quad
\{K,L_\alpha\}=0.$$ At the same time, these operators satisfy the following anticommutation relations: $$\{L_{\alpha},L_{\beta}\}=4i(J_{\mu}\gamma^{\mu})_{\alpha\beta}.
\label{llanti}$$ Hence, operator (\[lab\]) is the ‘square root’ operator of the $\overline{\rm SL(2,R)}$ generators (\[jmu\]). Calculating the commutators of $L_\alpha$ with $J_\mu$ being the generators of the (2+1)-dimensional Lorentz group, we get the relation: $$[J_\mu,L_\alpha]=\frac{1}{2}(\gamma_\mu)_\alpha{}^{\beta}L_\beta,
\label{jlcom}$$ which means that the introduced operators (\[lab\]) indeed form the (2+1)-dimensional spinor. Moreover, taking into account (anti)commutation relations (\[alg\]), (\[llanti\]) and (\[jlcom\]), we conclude that the operators $J_{\mu}$ and $L_\alpha$ form the $osp(1|2)$ superalgebra [@osp] with the Casimir operator $$C=J^{\mu}J_{\mu}-\frac{i}{8}L^{\alpha}L_{\alpha}=
\frac{1}{16}(1-\nu^2).
\label{ospcas}$$ This, in turn, means that we have constructed the generalization of the well known representation of $osp(1|2)$ superalgebra with $C=1/16$, realized by the ordinary bosonic oscillator ($\nu=0$) [@next; @macmaj], to the case of $C<1/16$ ($\nu\neq 0$) (see also ref. [@mac]).

Having the spinor object $L_\alpha$, which is a ‘square root’ operator of $J_\mu$, we can construct a covariant spinor linear differential operator with dimensionality of mass of the following 