Finite dimensional representations of \(\Gamma(\sigma_ 1,\sigma_ 2,\sigma_ 3)\)
The algebra considered here is the Lie superalgebra \(G= \Gamma (\sigma_1, \sigma_2, \sigma_3)\), which is denoted by \(D(2, 1; \alpha)\) in Kac's notation [\textit{V. G. Kac}, Adv. Math. 26, 8-96 (1977; Zbl 0366.17012)]. Using the technique of Bernstein, Gelfand and Gelfand the author gives a list of singly generated finite dimensional indecomposable representations for \(G\), and shows that any finite dimensional representation of \(G\) is a quotient of a direct sum of some representations from the list. Essentially, this list consists of the irreducible highest weight \(G\)-modules and of indecomposable \(G\)-modules of which the character is a sum of characters of irreducible so-called atypical modules.
scientific article; zbMATH DE number 701279