Boson representations, non-standard quantum algebras and contractions

A Gelfan'd-Dyson mapping is used to generate a one-boson realization for the non-standard quantum deformation of sl(2, R) which directly provides its infinite- and finite-dimensional irreducible representations. Tensor product decompositions are worked out for some examples. Relations between contraction methods and boson realizations are also explored in several contexts. So, a class of two-boson representations for the non-standard deformation of sl(2, R) is introduced and contracted to the non-standard quantum (1+1) Poincare representations. Likewise, a quantum extended Hopi sl(2, R) algebra is constructed and non-standard quantum oscillator algebra representations are obtained from it by means of another contraction procedure.