PROPOSITION 8.19. Let X be the complex Grassmannian with m, n 2. Let

8. Relations among forms on the complex Grassmannians

The results of this section are used only to prove Proposition 8.5 and the equalities (8.47) and (8.48). They do not enter into any of our other proofs and are presented only for the sake of completeness.

From the preceding equality and the relation (8.102), we obtain the first formula of (8.96). This completes the proof of Lemma 8.21.

9. The complex Grassmannians