  The vector system of linear differential equations for a field with arbitrary
fractional spin is proposed using infinite-dimensional half-bounded unitary
representations of the $\overline{SL(2,R)}$ group. In the case of
$(2j+1)$-dimensional nonunitary representations of that group, $0<2j\in Z$,
they are transformed into equations for spin-$j$ fields. A local gauge symmetry
associated to the vector system of equations is identified and the simplest
gauge invariant field action, leading to these equations, is constructed.
