Generalised Jantzen filtration of Lie superalgebras I

Details Generalised Jantzen filtration of Lie superalgebras I Generalised Jantzen filtration of Lie superalgebras I

2010-01-07

arxiv.org/abs/1001.1033v3

Mathematics

Representation Theory

This is the final version to appear in the Journal of European Math Society. LaTeX, 31 pages

Scientific paper

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.

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