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Complete sets of representations of classical Lie superalgebras

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Abstract

Descriptions of the complete sets of irreducible highest-weight modules over complex classical simple Lie superalgebras are recorded. It is further shown that the finite-dimensional irreducible modules over a (not necessarily classical simple) finite-dimensional complex Lie superalgebra form a complete set if and only if the even part of the Lie superalgebra is reductive and the universal enveloping superalgebra is semiprime.

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Letzter, E.S., Musson, I.M. Complete sets of representations of classical Lie superalgebras. Lett Math Phys 31, 247–253 (1994). https://doi.org/10.1007/BF00761716

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