Structure of polynomial representations for orthosymplectic Lie superalgebras

Details Structure of polynomial representations for orthosymplectic Lie superalgebras Structure of polynomial representations for orthosymplectic Lie superalgebras

2010-01-20

arxiv.org/abs/1001.3474v1

Mathematics

Representation Theory

36 pages

Scientific paper

Orthosymplectic Lie superalgebras are fundamental symmetries in modern physics, such as massive supergravity. However, their representations are far from being thoroughly understood. In the present paper, we completely determine the structure of their various supersymmetric polynomial representations obtained by swapping bosonic multiplication operators and differential operators in the canonical supersymmetric polynomial representations. In particular, we obtain certain new infinite-dimensional irreducible representations and new composition series of indecomposable representations for these algebras.

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