Quantum Deformation of the Grassmannian Manifold

Ž . In this paper we work out a deformation of G r, n , the grassmannian of r-subspaces in a vector space of dimension n over a field k of characteristic 0. Ž . Ž . G r, n is deformed as an homogeneous space for SL k , the special linear group n n w Ž .x Ž . of k ; this means that k G r, n , the coordinate ring of G r, n , gets deformed w x Ž . together with with the coaction of k SL , the coordinate ring of SL k , on it. n n Our deformation comes together with a coaction of the corresponding deformation Ž . of SL k . At the end we give an explicit presentation of the deformed grassmann nian, in terms of generators and relations. Q 1999 Academic Press