Generalised Jantzen filtration of Lie superalgebras. I
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Publication:437813
DOI10.4171/JEMS/328zbMATH Open1295.17008arXiv1001.1033OpenAlexW2963646050MaRDI QIDQ437813
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Publication date: 20 July 2012
Published in: (Search for Journal in Brave)
Abstract: A Jantzen type filtration for generalised Varma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac module 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. Furthermore, the length of the Jantzen filtration for any Kac module is determined explicitly in terms of the degree of atypicality of the highest weight. These results are applied to obtain a detailed description of the submodule lattices of Kac modules.
Full work available at URL: https://arxiv.org/abs/1001.1033
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