$\overline{SL}(4,R)$ Embedding for a 3D World Spinor Equation

A generic-curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the $\overline{SL}(n,R)$ group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved by embedding $\overline{SL}(3,R)$ vector operator $X_{\mu }$, that plays a role of Dirac’s ${\gamma }_{\mu }$ matrices, into $\overline{SL}(4,R)$. Decomposition of the unitary irreducible spinorial $\overline{SL}(4,R)$ representations gives rise to an explicit form of the infinite $X_{\mu }$ matrices.