Towards the Green correspondence for supergroups

2025/07/14 by Entova-Aizenbud, Inna, Serganova, Vera, Sherman, Alex
#17B10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.09912

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.

Citations

• Sylow theorems for supergroups
• It takes two spectral sequences
• Localization theorem for homological vector fields
• The Duflo-Serganova functor, vingt ans après
• On supergroups and their semisimplified representation categories
• Cohomology and support varieties for Lie superalgebras

Related

• Solvability and nilpotency for algebraic supergroups
• Semisimplifications and representations of the General Linear Supergroup
• Quotients of complex algebraic supergroups
• Quotients in super-symmetry: formal supergroup case
• The Green correspondence for SL(2,p)