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Algebra Seminar
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Alison Parker
University of Sydney

Higher extensions for SL2(k)

Friday 24th September, 12:05-12:55pm, Carslaw 175.

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 characteristic. 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.