Extensions de foncteurs simples*

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Let ℱ be the category of functors from finite Fp-vector spaces to Fp-vector spaces. We prove here that there is no nontrivial self-extension for any simple object S in ℱ i.e. that Ext1ℱ(S, S) = 0 To obtain this result, we show that the injective envelope of Sin a certain subcategory is a direct summand of a very explicit functor. The main ingredient is the behavior of the ‘difference’ functor Δ: ℱ → ℱ on S and on Schur functors. The appendix contains a description of these functors which is used to describe the lowest homogeneous nontrivial factor of ΔiS

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