Abstract
Explicit realizations of the quantum groups GLp,q(2) and GLp,q(1 mod 1) corresponding to unimodular values of the deformation parameters p and q are given in terms of the canonically conjugate (X, P) operators, using the Heisenberg-Weyl commutation relations. Matrix representations are also discussed. Some observations are made on similar realizations of the non-commutative coordinate spaces on which the quantum groups act as endomorphisms.