التفاصيل البيبلوغرافية
| العنوان: |
Khovanov algebras for the periplectic Lie superalgebras |
| المؤلفون: |
Nehme, Jonas |
| المصدر: |
Int. Math. Res. Notices , Vol. 2024, No. 22 |
| سنة النشر: |
2023 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Representation Theory, Mathematics - Quantum Algebra, 17B10 |
| الوصف: |
The periplectic Lie superalgebra $\mathfrak{p}(n)$ is one of the most mysterious and least understood simple classical Lie superalgebras with reductive even part. We approach the study of its finite dimensional representation theory in terms of Schur--Weyl duality. We provide an idempotent version of its centralizer, i.e. the super Brauer algebra. We use this to describe explicitly the endomorphism ring of a projective generator for $\mathfrak{p}(n)$ resembling the Khovanov algebra of [BS11a]. We also give a diagrammatic description of the translation functors from [BDE19] in terms of certain bimodules and study their effect on projective, standard, costandard and irreducible modules. These results will be used to classify irreducible summands in $V^{\otimes d}$, compute $\mathrm{Ext}^1$ between irreducible modules and show that $\mathfrak{p}(n)$-mod does not admit a Koszul grading. |
| نوع الوثيقة: |
Working Paper |
| DOI: |
10.1093/imrn/rnae230 |
| URL الوصول: |
http://arxiv.org/abs/2312.08390 |
| رقم الانضمام: |
edsarx.2312.08390 |
| قاعدة البيانات: |
arXiv |