SMS scnews item created by Anne Thomas at Fri 1 Apr 2011 1021
Type: Seminar
Distribution: World
Expiry: 8 Apr 2011
Calendar1: 8 Apr 2011 1205-1255
CalLoc1: Carslaw 175
Auth: athomas(.pmstaff;2039.2002)@p615.pc.maths.usyd.edu.au

# 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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