Duality properties for induced and coinduced representations in positive characteristic

TL;DR

This paper investigates duality properties of coinduced representations in Lie superalgebras over fields of positive characteristic, extending previous results from Lie algebras and characteristic zero to positive characteristic cases.

Contribution

It establishes a duality property for coinduced representations in positive characteristic Lie superalgebras, generalizing earlier results to new algebraic settings.

Findings

Proves a duality property for coinduced representations in positive characteristic

Links between coinduced and induced representations in restricted Lie superalgebras

Extends known duality results to broader algebraic contexts

Abstract

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