On the construction of covariant differential calculi on quantum homogeneous spaces

Let A be a coquasitriangular Hopf algebra and X the subalgebra of A generated by a row of a matrix corepresentation u or by a row of u and a row of the contragredient corepresentation u(c). In the paper left-covariant first order differential calculi on the quantum group A are constructed and the corresponding induced calculi on the left quantum space X are described. The main tool for these constructions are the L-functionals associated with u. The results are applied to the quantum homogeneous space GL(q)(N)/GL(q)(N - 1). (C) 1999 Elsevier Science B.V. All rights reserved.