JournalsjemsVol. 14, No. 4pp. 1103–1133

Generalised Jantzen filtration of Lie superalgebras I

  • Yucai Su

    University of Scinece and Technology of China, Hefei, China
  • Ruibin Zhang

    University of Sydney, Australia
Generalised Jantzen filtration of Lie superalgebras I cover
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Abstract

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.

Cite this article

Yucai Su, Ruibin Zhang, Generalised Jantzen filtration of Lie superalgebras I. J. Eur. Math. Soc. 14 (2012), no. 4, pp. 1103–1133

DOI 10.4171/JEMS/328