Hypercubic Decomposition of Verma Supermodules and Semibricks Realizing the Khovanov Algebra of Defect One

Abstract

We study some variants of Verma modules of basic Lie superalgebras obtained via changing Borel subalgebras. These allow us to demonstrate that the principal block of \(\mathfrak{gl}(1|1)\) is realized as (non-Serre) full subcategories of any atypical block of BGG category \( \mathcal{O} \) of basic Lie superalgebras.

This paper has been withdrawn because its content has beeen largely subsumed by arxiv:2502.14274, which provides a more complete and improved treatment