The two-variable coherent states of the quantum algebra su(q)(1,1)

By means of the k-order q-boson realizations of su(q)(1, 1), a new kind of q-coherent states, the two-variable coherent states, are introduced for the quantum algebra su(q)(1, 1). They are relative to a definite irreducible representation of su(q)(1, 1) and shown to satisfy a completeness relation in a subspace of q-boson's Fock space. With the help of these coherent states the z-representation, representation in functional space, for su(q)(1, 1) is also discussed.