  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".
