Differential Calculus on q-Deformed Grassmann Manifolds*)

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Covariant first order differential calculus over quantum complex Grassmann manifolds is considered. It is shown by a Pusz-Woronowicz type argument that under restriction to calculi close to the classical Kähler differentials there exist exactly two such calculi for the homogeneous coordinate ring. Complexification and localization procedures are used to induce covariant first order differential calculi over the quantum Grassmann manifolds.

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