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Orthosymplectic superalgebras in mathematics and science


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Farmer, R J(Richard Joseph) 1984 , 'Orthosymplectic superalgebras in mathematics and science', PhD thesis, University of Tasmania.

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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

Item Type: Thesis - PhD
Authors/Creators:Farmer, R J(Richard Joseph)
Keywords: Lie algebras, Algebra
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Copyright 1984 the Author - The University is continuing to endeavour to trace the copyright
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Thesis (Ph.D.)--University of Tasmania, 1985. Includes bibliographies

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