On the Bernstein-Gel'fand-Gel'fand correspondence and a result of Eisenbud, Fløystad, and Schreyer

Abstract

We show that a combination between a remark from the well known note of I.N. Bernstein, I.M. Gel'fand and S.I. Gel'fand and the idea, systematically investigated in a recent work of D. Eisenbud, G. Fløystad and F.-O. Schreyer, of taking Tate resolution over exterior algebras leads to quick proofs of the main results of these two papers. This combination is expressed by a lemma which we prove directly using the cohomology of invertible sheaves on a projective space.