Towards the Green correspondence for supergroups

TL;DR

This paper extends the Green correspondence to complex algebraic supergroups, establishing a link between specific indecomposable representations of the supergroup and those of the normalizer of a Sylow subgroup.

Contribution

It introduces a novel version of the Green correspondence applicable to supergroups, bridging representation theory of supergroups and their Sylow subgroups.

Findings

Established a Green correspondence for complex algebraic supergroups.

Constructed a correspondence between indecomposable representations of G and its Sylow subgroup normalizer.

Provided foundational results for supergroup representation theory.

Abstract

We prove a version of the Green correspondence for complex algebraic supergroups, constructing a correspondence between certain indecomposable representations of G and the normalizer of a Sylow subgroup of G.