GLh​(n)×GLh′​(m)-covariant (hh')-bosonic (or (hh')-fermionic)
algebras Ahh′±​(n,m) are built in terms of the corresponding R_h
and Rh′​-matrices by contracting the GLq​(n)×GLq±1​(m)-covariant q-bosonic (or q-fermionic) algebras Aq±(α)​(n,m), α=1,2. When using a basis of Aq±(α)​(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 Uq​(gl(n))⊗Uq±1​(gl(m)), a contraction limit only exists for n,m∈{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
Uh​(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 Ah±​(2,1).Comment: LaTeX, uses amssym.sty, 24 pages, no figure, to be published in Int.
J. Theor. Phy