A detailed summary is given of the structure of singular indecomposable representations of si (2,ℂ), as developed by Gel'fand and Ponomarev [Usp. Mat. Nauk 23, 3 (1968); translated in Russ. Math. Surveys 23, 1 (1968)]. A variety of four-vector operators Γμ is constructed, acting within direct sums of such representations, including some with nonsingular Γ0. Associated wave equations of Gel'fand-Yaglom type are considered that admit timelike solutions and lead to mass-spin spectra of the Majorana type. A subclass of these equations is characterized in an invariant way by obtaining basis-independent expressions for the commutator and anticommutator of Γμ and Γν. A brief discussion is given of possible applications to physics of these equations and of others in which nilpotent scalar operators appear
