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arXiv · 1303.4797

Generalised Jantzen filtration of Lie superalgebras II: the exceptional cases

Yucai Su·R. B. Zhang
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Abstract

Let $g$ be an exceptional Lie superalgebra, and let $p$ be the maximal parabolic subalgebra which contains the distinguished Borel subalgebra and has a purely even Levi subalgebra. For any parabolic Verma module in the parabolic category $O^p$, it is shown that the Jantzen filtration is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan-Lusztig polynomials. An explicit description of the submodule lattices of the parabolic Verma modules is given, and formulae for characters and dimensions of the finite dimensional simple modules are obtained.

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BibTeXRIS

Yucai Su, R. B. Zhang. 2013-03-20. Generalised Jantzen filtration of Lie superalgebras II: the exceptional cases. https://arxiv.org/abs/1303.4797

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