Indecomposable representations of ${\rm osp}(3,2)$, $D(2,1;\alpha)$ and $G(3)$.

Jérôme Germoni

We classify the finite-dimensional representations of the Lie superalgebras ${\rm osp}(3,2)$, $D(2,1;\alpha)$ (the one-parameter family of deformations of ${\rm osp}(4,2)$) and $G(3)$. In short, indecomposable representations in the non-trivial blocks are, up to isomorphism and duality, naturally parametrized by positive roots of an infinite Dynkin diagram of type $D_\infty$ or $A^\infty_\infty$. From this result we can deduce the representation type of all basic classical Lie superalgebras but $F(4)$.

Mots clés: Lie superalgebra; indecomposable representation

Domaines: Théorie des représentations [math.RT]

Jérôme Germoni. Indecomposable representations of ${\rm osp}(3,2)$, $D(2,1;\alpha)$ and $G(3)$.. Boletin de la Academia Nacional de Ciencias, 2000, 65, pp. 147-163. ⟨hal-00002750⟩