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1983•Journal of Mathematical PhysicsRequires access

SU(2)×SU(2) shift operators and representations of SO(5)

J. W. B. Hughes

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Abstract

SU(2)×SU(2) shift operators analogous to the SU(2) shift operators developed and used by the author for the classification and analysis of representations of Lie algebras in an SU(2) or SO(3) basis are obtained for the SU(2)×SU(2) Lie algebra in the case where one has an additional set of operators forming an irreducible four-dimensional tensor representation of SU(2)×SU(2). The shift operators obtained are used to treat the representations of SO(5) in an SU(2)×SU(2) basis.

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What this paper is about

SU(2)×SU(2) shift operators analogous to the SU(2) shift operators developed and used by the author for the classification and analysis of representations of Lie algebras in an SU(2) or SO(3) basis are obtained for the SU(2)×SU(2) Lie algebra in the case where one has an additional set of operators forming an irreducible four-dimensional tensor representation of SU(2)×SU(2). The shift operators obtained are used to treat the representations of SO(5) in an SU(2)×SU(2) basis.

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Available abstract

SU(2)×SU(2) shift operators analogous to the SU(2) shift operators developed and used by the author for the classification and analysis of representations of Lie algebras in an SU(2) or SO(3) basis are obtained for the SU(2)×SU(2) Lie algebra in the case where one has an additional set of operators forming an irreducible four-dimensional tensor representation of SU(2)×SU(2). The shift operators obtained are used to treat the representations of SO(5) in an SU(2)×SU(2) basis.

Key concepts: Representation theory of SU, Irreducible representation, Lie algebra, Fundamental representation, (g,K)-module, Mathematics, Algebra over a field, Lie group

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