Chih-Whi Chen
Published 2021-08-05Version 1
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.
Semisimplicity of the $DS$ functor for the orthosymplectic Lie superalgebra
Lower defect groups and vertices of simple modules
On The Cohomology of $\mathrm{SL}_2$ with Coefficients in a Simple Module
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