NONSTANDARD GLh(n) QUANTUM GROUPS AND CONTRACTION OF COVARIANT q-BOSONIC ALGEBRAS*)

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Abstract

GLh(n) × GLh(m)-covariant h-bosonic algebras are built by contracting the GLq(n) × GLq(m)-covariant q-bosonic algebras considered by the present author some years ago. Their defining relations are written in terms of the corresponding Rh-matrices. Whenever n = 2, and m = 1 or 2, it is proved by using Uh(sl(2)) Clebsch-Gordan coefficients that they can also be expressed in terms of coupled commutators in a way entirely similar to the classical case. Some Uh(sl(2)) rank-(1/2) irreducible tensor operators, recently constructed by Aizawa in terms of standard bosonic operators, are shown to provide a realization of the h-bosonic algebra corresponding to n = 2 and m = 1.

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