Witt groups of Grassmann varieties

Journal of algebraic geometry, 21, issue 4, 2012, p. 601-642
(1^st online appearance of the preprint on the 21-7-2008)

We compute the total Witt group of (split) Grassmann varieties over any regular base X. The answer is a free module over the total Witt ring of X. We provide an explicit basis for this free module, which is indexed by a special class of Young diagrams, that we call even Young diagrams. The proof uses the techniques developed in Geometric description of the connecting homomorphism for Witt groups.