Generalised Jantzen filtration of Lie Superalgebras
主 题: Generalised Jantzen filtration of Lie Superalgebras
报告人: R.B. ZHANG (University of Sydney)
时 间: 2010-03-31 下午3:30-4:30
地 点: 理科一号搂1275
A Jantzen type filtration for generalised Varma modules of Lie superalgebras is introduced and its properties are developed. In the case of type I Lie superalgebras, we show 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 led to a detailed description of the submodule lattices of Kac modules. This is joint work with Yucai Su.