Orthosymplectic superalgebras in mathematics and science

This thesis is devoted to the study of the representation theory of orthosymplectic superalgebras and their applications to physical theories. Techniques are developed to educe typical and atypical finite-dimensional, irreducible representations of orthosymplectic superalgebras. These include superfield and weight space procedures which are illustrated for several low-rank orthosymplectic superalgebras. Young supertableaux are used to enumerate finite-dimensional typical, tensor representations and spinor representations of OSp(M/N), and atypical, tensor representations of OSp(2/2), OSp(3/2) and OSp(4/2). Relations between Kac-Dynkin and supertableau labels are obtained and used to present conditions on diagram shape, necessary and sufficient for atypicality. Modification rules for typical supertableaux of OSp(M/N), and for atypical supertableaux of OSp(2/2), OSp(3/2) and OSp(4/2) are presented. Dimension formulae, in diagram notation, are discussed for typical, representations of OSp(M/N). New superfield realisations are presented for the determination of infinite-dimensional irreducible representations of N-extended super-Poincare algebras with central charges. These are illustrated for the N=2 extended super-Poincare algebra with one central charge. Finally, a discussion of the roles played by orthosymplectic supergroups in some physical theories is presented.