Representations of the Lie superalgebras \({\mathfrak gl}(n,m)\) and Q(n) on the space of tensors. (English. Russian original) Zbl 0542.17002
Funct. Anal. Appl. 18, 70-72 (1984); translation from Funkts. Anal. Prilozh. 18, No. 1, 80-81 (1984).
The author extends the classical method of H. Weyl for obtaining all the irreducible finite-dimensional representations of simple Lie algebras of type \(A_ n\) to the superalgebras of types \({\mathfrak gl}(n,m)\) and Q(n). As a consequence, the character formula of the irreducible finite- dimensional representations of Q(n) in a tensor space is derived.
Reviewer: W.Guz
MSC:
| 17A70 | Superalgebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
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