Abstract: | We construct representations of the quantum algebras Uq,q(gl(n)) and Uq,q(sl(n)) which are in duality with the multiparameter quantum groups GLqq(n), SLqq(n), respectively. These objects depend on n(n − 1)/2+ 1 deformation parameters q, qij (1 ≤ i< j ≤ n) which is the maximal possible number in the case of GL(n). The representations are labelled by n − 1 complex numbers ri and are acting in the space of formal power series of n(n − 1)/2 non-commuting variables. These variables generate quantum flag manifolds of GLqq(n), SLqq(n). The case n = 3 is treated in more detail. |