Higher extensions between modules for SL₂

الأصل · EN

We calculate Ext*SL₂(k)(Δ(λ), Δ(μ)), Ext*SL₂(k)(L(λ), Δ(μ)), Ext*SL₂(k)(Δ(λ), L(μ)), and Ext*SL₂(k)(L(λ), L(μ)), where Δ(λ) is the Weyl module of highest weight λ, L(λ) is the simple SL₂(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 E₂ page of any spectral sequence to be the same as the E∞ page.