  For bicovariant differential calculi on quantum matrix groups a
generalisation of classical notions such as metric tensor, Hodge operator,
codifferential and Laplace-Beltrami operator for arbitrary k-forms is given.
Under some technical assumptions it is proved that Woronowicz' external algebra
of left-invariant differential forms either contains a unique form of maximal
degree or it is infinite dimensional. Using Jucys-Murphy elements of the Hecke
algebra the eigenvalues of the Laplace-Beltrami operator for the Hopf algebra
O(SLq(N)) are computed.
