Finite irreducible modules over the conformal superalgebras K'_4 and CK_6

In this thesis we classify all finite irreducible modules over the conformal superalgebra K'_4 by means of their correspondence with irreducible finite conformal modules over the annihilation superalgebra associated with K'_4. We obtain that degenerate Verma modules over the annihilation superalgebra associated with K'_4 are part of infinite complexes and the number of these complexes is infinite; we compute the homology of these complexes with techniques of spectral sequences and provide an explicit realization of all irreducible quotients. We prove a technical result, stated by Boyallian, Kac and Liberati, on singular vectors of degenerate Verma modules over the annihilation superalgebra associated with CK_6. We start the computation of the homology of the diagram of infinite complexes of degenerate Verma modules for CK_6 found by Boyallian, Kac and Liberati.