Generalised Jantzen filtration of Lie superalgebras I.
Fri, 01/08/2010 - 16:01 — SomNambul
link: http://arxiv.org/abs/1001.1033
Abstract
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.
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