On semisimplicity of Jantzen middles for the periplectic Lie superalgebra

Abstract

We prove that an integral block of the category $\mathcal{O}$ of the periplectic Lie superalgebra contains a non-semisimple Jantzen middle if and only if it contains a simple module of atypical highest weight. As a consequence, every atypical integral block of $\mathcal{O}$ does not admit a Kazhdan-Lusztig theory in the sense of Cline, Parshall and Scott.

arXiv comment18 pages

References in corpus (6)

• Tensor product categorifications and the super Kazhdan-Lusztig conjecture
• On representations of the Lie superalgebra p(n)
• Equivalence of blocks for the general linear Lie superalgebra
• The primitive spectrum of basic classical Lie superalgebras
• Duflo-Serganova functor and superdimension formula for the periplectic Lie superalgebra
• Gorenstein homological algebra for rngs and Lie superalgebras