Higher extensions between modules for SL_2

Abstract

We calculate Ext^*_{SL_2(k)}(Δ(λ), Δ(μ)), Ext^*_{SL_2(k)}(L(λ), Δ(μ)), Ext^*_{SL_2(k)}(Δ(λ), L(μ)), and Ext^*_{SL_2(k)}(L(λ), L(μ)), where Δ(λ) is the Weyl module of highest weight λ, L(λ) is the simple SL_2(k)-module of highest weight λand our field k is algebraically closed of positive characteristic. We also get analogous results for the Dipper-Donkin quantisation. To do thus we construct the Lyndon-Hochschild-Serre spectral sequence in a new way, and find a new condition for the E_2 page of any spectral sequence to be the same as the E_\infty page.