- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:07
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
14
2012
4
Generalised Jantzen filtration of Lie superalgebras I
Yucai
Su
University of Scinece and Technology of China, HEFEI, CHINA
R.B.
Zhang
University of Sydney, SYDNEY, AUSTRALIA
Lie superalgebras, Jantzen filtrations, Verma modules; Kazhdan–Lusztig polynomials
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.
Nonassociative rings and algebras
General
1103
1133
10.4171/JEMS/328
http://www.ems-ph.org/doi/10.4171/JEMS/328