Multiboson Expansions for the q-Oscillator and $SU(1,1{)}_q$

Abstract

All the hermitian representations of the ``symmetric" $q$-oscillator are obtained by means of expansions. The same technique is applied to characterize in a systematic way the $k$-order boson realizations of the $q$-oscillator and $su(1,1{)}_q$. The special role played by the quadratic realizations of $su(1,1{)}_q$ in terms of boson and $q$-boson operators is analysed and clarified.

arXiv comment13 pages, AMS-TEX file, UVA/93-92