Bernstein-Gel'fand-Gel'fand reciprocity and indecomposable projective modules for classical algebraic supergroups

TL;DR

This paper establishes a BGG reciprocity law for finite-dimensional modules over certain algebraic supergroups, introducing Euler characteristics as standard modules and describing indecomposable projectives in the orthosymplectic case.

Contribution

It proves a BGG reciprocity law for algebraic supergroups and characterizes indecomposable projective modules via Euler characteristics in the orthosymplectic case.

Findings

Proved BGG reciprocity law for algebraic supergroups

Identified Euler characteristics as standard modules

Described indecomposable projective modules in orthosymplectic case

Abstract

We prove a BGG type reciprocity law for the category of finite dimensional modules over algebraic supergroups satisfying certain conditions. The equivalent of a standard module in this case is a virtual module called Euler characteristic due to its geometric interpretation. In the orthosymplectic case, we also describe indecomposable projective modules in terms of those Euler characteristics.