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The title says it all: What are the exactness properties of Schur Functors?


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Can you be specific what do you mean by Schur functor. I presume you are saying the Schur functor related to Schur algebra $S(n,r)$ and symmetric group algebra $F\Sigma_r$, or any similar system such as the functor arising from quasi-hereditary cover of an algebra. In that case, $F\Sigma_r = e S(n,r) e$ for some idempotent $e$ and the Schur functor is given by $e(-)$. Well, then exactness follows since $e(-) = \mathrm{Hom}_{S(n,r)} (S(n,r)e, - )$, which is an exact functor. –  Aaron Nov 20 '12 at 18:42

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