Witt groups of Grassmann varieties

Abstract

We compute the total Witt groups 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.Comment: 31 pages, 16 figures. Final version. Complies with the new formalism on total Witt groups recently developed by the authors (arXiv:1104.5051