Witt groups of spinor varieties

We show that Witt groups of spinor varieties (aka.\ maximal isotropic Grassmannians) can be presented by combinatorial objects called even shifted young diagram. Our method relies on the Blow-up setup of Balmer-Calm`es, and we investigate the connecting homomorphism of the localization sequence via the projective bundle formula of Walter-Nenashev, the projection formula of Calm`es-Hornbostel and the excess intersection formula of Fasel.