2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216529The SW(3/2,3/2,2) superconformal algebra is a W algebra with two free parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2. The algebra is proved to be the symmetry algebra of the coset (su(2)+su(2)+su(2))/su(2). At the central charge c=21/2 the algebra coincides with the superconformal algebra associated to manifolds of G_2 holonomy. The unitary minimal models of the SW(3/2,3/2,2) algebra and their fusion structure are found. The spectrum of unitary representations of the G_2 holonomy algebra is obtained.34 pages, 2 figures, latex; v2: added examples in appendix D; v3: published version, corrected typosHigh Energy Physics - TheoryMathematical Physicstext