Geodesic
Generalised Jantzen filtration of Lie superalgebras I
Journal of the European Mathematical Society, Tome 14 (2012) no. 4, pp. 1103-1133

Voir la notice de l'article provenant de la source EMS Press

A Jantzen type filtration for generalised Verma 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.
DOI : 10.4171/jems/328
Classification : 17-XX, 00-XX
Keywords: Lie superalgebras, Jantzen filtrations, Verma modules; Kazhdan–Lusztig polynomials 
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     author = {Yucai Su and Ruibin Zhang},
     title = {Generalised {Jantzen} filtration of {Lie} superalgebras {I}},
     journal = {Journal of the European Mathematical Society},
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     doi = {10.4171/jems/328},
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}
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Yucai Su; Ruibin Zhang. Generalised Jantzen filtration of Lie superalgebras I. Journal of the European Mathematical Society, Tome 14 (2012) no. 4, pp. 1103-1133. doi: 10.4171/jems/328

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