Abstract
In the present note we touch shortly certain points from the representation theory of the basic Lie superalgebras (LS’s). We consider in more details the special linear Lie superalgebra(LS) sl(1,n) and indicate how one can introduce a concept of a Gel’fand-Zetlin basis in the finite-dimensional irreducible modules (fidirmods)1 of sl(1,n).
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Throughout the paper we use the following abbreviations and notations: fidermod(s) - finite-dimensional irreducible modules(s) LS,LSs - Lie superalgebra, Lie superalgebras LA,LAs-Lie algebra, Lie algebras [,] - product in the LS.[m]i = [m1i m2i...,mii], i = 1,2,..., n [m]n+1 = [m1,n+1,m2,n+1,..., mn,n+1]
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Paley, T.D. (1986). On the Representations of the Basic Lie Superalgebras: Gel’fand Zetlin Basis for sl(1,n). In: Gruber, B., Lenczewski, R. (eds) Symmetries in Science II. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1472-2_39
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DOI: https://doi.org/10.1007/978-1-4757-1472-2_39
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