Equivalence of blocks for the general linear Lie superalgebra

TL;DR

This paper introduces a reduction method that establishes an equivalence between blocks of category O for general linear Lie superalgebras and those for simpler algebraic structures, aiding classification and analysis.

Contribution

It develops a reduction procedure that shows equivalence of blocks in category O for general linear Lie superalgebras to blocks of simpler algebras, and proves indecomposability of these blocks.

Findings

Reduction procedure for blocks of category O

Equivalence of blocks across different algebra structures

Proof of indecomposability of blocks

Abstract

We develop a reduction procedure which provides an equivalence (as highest weight categories) from an arbitrary block (defined in terms of the central character and the integral Weyl group) of the BGG category O for a general linear Lie superalgebra to an integral block of O for (possibly a direct sum of) general linear Lie superalgebras. We also establish indecomposability of blocks of O.