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Let $k$ be a field of positive characteristic $p>2$. We prove a dualityproperty concerning the kernel of coinduced representations of Liesuperalgebras. This property was already proved by M. Duflo for Lie algebras inany characteristic under more restrictive finiteness conditions. It was thengeneralized to Lie superalgebras in characteristic 0 in previous works of theauthor. In a second part of the article, we study the links between coinducedrepresentations and induced representations in the case of restricted Liesuperalgebras.

Duality properties for induced and coinduced representations in positive characteristic