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Representations of classical Lie superalgebras of type I. (English) Zbl 0849.17030

Summary: An explicit description of a generic irreducible module (possibly infinite-dimensional and not necessarily diagonalizable over some Cartan subsuperalgebra) over a finite-dimensional classical Lie superalgebra \({\mathcal G}\) of type I is given in terms of its irreducible \({\mathcal G}_0\)-submodules. For a finite-dimensional module the result reduces to a character formula, proved earlier by J. Bernstein and D. Leites for the Lie superalgebras \(\text{gl} (1+ m\varepsilon)\), \(\text{gl} (m+ \varepsilon)\), \(\text{osp} (2+ n\varepsilon)\) [C. R. Acad. Bulg. Sci. 33, 1049-1051 (1980; Zbl 0457.17002)]. In the finite-dimensional case a character formula for another class of, so-called relatively typical, irreducible modules is also proved and illustrated by explicit examples.

MSC:

17B70 Graded Lie (super)algebras
17A70 Superalgebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)

Citations:

Zbl 0457.17002
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References:

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