Boson–fermion representations of Lie superalgebras: The example of osp(1,2)

A method for constructing infinite‐dimensional representations of Lie superalgebras employing boson representations of their Lie subalgebras is outlined. As an example the osp(1,2) superalgebra is considered; explicit formulae for its generators in terms of one pair of boson operators, at most one p...

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Published in:Journal of mathematical physics 1982-03, Vol.23 (3), p.350-353
Main Authors: Blank, Jiří, Havlíček, Miloslav, Exner, Pavel, Lassner, Wolfgang
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Language:English
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description A method for constructing infinite‐dimensional representations of Lie superalgebras employing boson representations of their Lie subalgebras is outlined. As an example the osp(1,2) superalgebra is considered; explicit formulae for its generators in terms of one pair of boson operators, at most one pair of fermion ones, and at most one parameter are obtained, the Casimir operator being represented by a multiple of unity. The restriction of these representations to the real form of osp(1,2) is skew‐symmetric in the even part and can be regarded as a natural generalization of skew‐symmetric representations of real Lie algebras. Some other aspects of the presented construction are discussed.
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title Boson–fermion representations of Lie superalgebras: The example of osp(1,2)
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