ON THE CLASSICAL LIMIT OF SOME Q-COMMUTATION RELATIONS

Two types of operators (I, II) are constructed in terms of bosonic qua ntum (q-)oscillator operators. These operators satisfy a relation anal ogous to the q-commutation relation for fermionic quantum (q-)oscillat ors. Both types of operators (I, II) can be identified with the fermio nic harmonic oscillator in the limit q --> 1 by exploiting the presenc e of certain arbitrary functions of the deformation parameter q. For I they may be identified as parameters of U(1) transformations while fo r II they correspond to parameters of GL(2,R) transformations. Appropr iate fermionic number operators in the limit q --> 1 are also construc ted.