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arXiv · 2108.02617

On semisimplicity of Jantzen middles for the periplectic Lie superalgebra

Chih-Whi Chen
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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.

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BibTeXRIS

Chih-Whi Chen. 2021-08-05. On semisimplicity of Jantzen middles for the periplectic Lie superalgebra. https://arxiv.org/abs/2108.02617

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