Representations of the Exceptional Lie superalgebra E(3,6): I. Degeneracy conditions

Details Representations of the Exceptional Lie superalgebra E(3,6): I. Degeneracy conditions Representations of the Exceptional Lie superalgebra E(3,6): I. Degeneracy conditions

2000-12-28

arxiv.org/abs/math-ph/0012049v1

Physics

Mathematical Physics

20 pages, LaTex

Scientific paper

Recently one of the authors obtained a classification of simple infinite-dimensional Lie superalgebras of vector fields which extends the well-known classification of E. Cartan in the Lie algebra case. The list consists of many series defined by simple equations, and of several exceptional superalgebras, among them E(3,6). In the article we study irreducible representations of the exceptional Lie superalgebra E(3,6). This superalgebra has s\ell(3)\times s\ell(2)\times g\ell(1) as the zero degree component of its consistent \ZZ-grading which leads us to believe that its representation theory has potential for physical applications.

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