Higher extensions between modules for [formula omitted]

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 ) ) , 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. 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 ∞ page.