Algebra Seminar: Zhang -- Jantzen filtration for Kac modules

The Algebra Seminar on Friday 8 April will be given by Ruibin Zhang.  

I will be overseas from 2 April until 7 May.  While I am away, Anthony Henderson will
host the seminar and lunch, and Andrew Mathas will be in charge of the webpage and
announcements.  Thank you to Anthony and Andrew for filling in.  

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Speaker: Ruibin Zhang (University of Sydney) 

Date: Friday 8 April 

Time: 12.05-12.55pm 

Venue: Carslaw 175 

Title: 

Jantzen filtration for Kac modules 

Abstract: 

A Jantzen type filtration is introduced for generalised Varma 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.  

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