2021
DOI: 10.48550/arxiv.2108.02617
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On semisimplicity of Jantzen middles for the periplectic Lie superalgebra

Abstract: We prove that an integral block of the category 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 O does not admit a Kazhdan-Lusztig theory in the sense of Cline, Parshall and Scott.

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