Witt groups of spinor varieties

Abstract

We compute Witt groups of maximal isotropic Grassmannians, aka. spinor varieties. They are examples of type D homogenuous varieties. Our method relies on the Blow-up setup of Balmer-Calmès, and we investigate the connecting homomorphism via the projective bundle formula of Walter-Nenashev, the projection formula of Calmès-Hornbostel and the excess intersection formula of Fasel. The computation in the Type D case can be presented by so called "even shifted young diagrams".