## University of Sydney Algebra Seminar

# Ruibin Zhang (University of Sydney)

## Friday 8 April, 12:05-12:55pm, Carslaw 175

### Jantzen filtration for Kac modules

A Jantzen type filtration is introduced for generalised Verma modules over Lie superalgebras. In the case of type I Lie superalgebras, we show that the generalized 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 equal to the degree of atypicality. These results led to a detailed description of the submodule lattices of Kac modules. This is joint work with Yucai Su.