$GL_h(n) \times GL_{ h'}(m)$-covariant (hh')-bosonic (or (hh')-fermionic) algebras ${ \cal A}_{ hh'\pm}(n,m)$ are built in terms of the corresponding R_h and $R_{ h'}$-matrices by contracting the $GL_q(n) \times GL_{ q^{ \pm1}}(m)$-covariant q-bosonic (or q-fermionic) algebras ${ \cal A}^{ (\alpha)}_{ q\pm}(n,m)$, $\alpha = 1, 2$. When using a basis of ${ \cal A}^{ (\alpha)}_{ q\pm}(n,m)$ wherein the annihilation operators are contragredient to the creation ones, this contraction procedure can be carried out for any n, m values. When employing instead a basis wherein the annihilation operators, as the creation ones, are irreducible tensor operators with respect to the dual quantum algebra $U_q(gl(n)) \otimes U_{ q^{ \pm1}}(gl(m))$, a contraction limit only exists for $n, m \in \{ 1, 2, 4, 6, ...\}$. For n=2, m=1, and n=m=2, the resulting relations can be expressed in terms of coupled (anti)commutators (as in the classical case), by using $U_h(sl(2))$ (instead of sl(2)) Clebsch-Gordan coefficients. Some U_h(sl(2)) rank-1/2 irreducible tensor operators, recently constructed by Aizawa, are shown to provide a realization of ${ \cal A}_{ h\pm}(2,1)$.
Categories: math.QA hep-th math-ph math.MP