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

Shunsuke Hirota

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

Representation Theory 2025-05-05 v4 Rings and Algebras

Authors: Shunsuke Hirota

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.

Keywords

Verma supermodule hypercubic decomposition Khovanov algebra Lie superalgebra BGG category semibricks defect one

Cite

@article{arxiv.2502.10987,
  title  = {Hypercubic Decomposition of Verma Supermodules and Semibricks Realizing the Khovanov Algebra of Defect One},
  author = {Shunsuke Hirota},
  journal= {arXiv preprint arXiv:2502.10987},
  year   = {2025}
}

Comments

This paper has been withdrawn because its content has beeen largely subsumed by arxiv:2502.14274, which provides a more complete and improved treatment

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

Abstract

Keywords

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