Vanishing cotangent cohomology for Pl\"ucker algebras

We use representation theory and Bott’s theorem to show vanishing of higher cotangent cohomology modules for the homogeneous coordinate ring of Grassmannians in the Pl"ucker embedding. As a biproduct we answer a question of Wahl about the cohomology of the square of the ideal sheaf for the case of Pl"ucker relations.