Boson representations, non-standard quantum algebras and contractions

Details Boson representations, non-standard quantum algebras and contractions Boson representations, non-standard quantum algebras and contractions

1996-11-25

arxiv.org/abs/q-alg/9611031v2

J.Phys. A30 (1997) 6797-6809

Mathematics

Quantum Algebra

21 pages, LaTeX; two new references added

Scientific paper

10.1088/0305-4470/30/19/018

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) Poincar\'e representations. Likewise, a quantum extended Hopf $sl(2,\R)$ algebra is constructed and the Jordanian $q$-oscillator algebra representations are obtained from it by means of another contraction procedure.

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