Higher extensions between modules for SL_2

Alison Parker

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 λ and our field k is algebraically closed of positive characteristic. We also get analogous results for the Dipper-Donkin quantisation.