University of Sydney
Higher extensions for SL2(k)
Friday 24th September, 12:05-12:55pm,
In this talk we review a variant of the Lyndon-Hochschild-Serre
spectral sequence for algebraic groups.
We use this to show that the E2 page of the spectral sequence
for the group Ext*(Delta(lambda),Delta(mu)) is the
same as the E-infinity page.
In particular we get a nice recursion formula for the Ext
group and so it may be completely calculated by this method.
Here Delta(lambda) is the Weyl module for SL2(k)
of highest weight lambda, mu is another highest weight
and k is an algebraically closed field of prime
We get similar results for Ext*(L(lambda),Delta(mu))
and Ext*(Delta(mu),L(lambda)) where L(lambda) is the
simple module of highest weight mu.
The talk will assume some familiarity with homological algebra
but none with spectral sequences.