BOSON REPRESENTATIONS, NONSTANDARD QUANTUM ALGEBRAS AND CONTRACTIONS

A Gelfan'd-Dyson mapping is used to generate a one-boson realization f or the non-standard quantum deformation of sl(2, R) which directly pro vides its infinite- and finite-dimensional irreducible representations . Tensor product decompositions are worked out for some examples. Rela tions between contraction methods and boson realizations are also expl ored 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-stand ard quantum oscillator algebra representations are obtained from it by means of another contraction procedure.