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-Calm`es, and we investigate the connecting homomorphism via the projective bundle formula of Walter-Nenashev, the projection formula of Calm`es-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.
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