Covariant (hh′)-deformed bosonic and fermionic algebras as contraction limits of q-deformed ones

GL(h)(n) X GL(h')(m)-covariant (hh')-bosonic [or (hh')-fermionic] algebras A(hh'+/-)(n, m) are built in terms of the corresponding R-h and R-h'-matrices by contracting the GL(q)(n) X GL(q+/-1)(m)-covariant q-bosonic (or q-fermionic) algebras A(q+/-)((alpha))(n, m), alpha = 1, 2. When using a basis of A(q+/-)((alpha))(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, like the creation ones, are irreducible tensor operators with respect to the dual quantum algebra U-q(gl(n)) X Uq+/-1(gl(m)), a contraction limit only exists for n, m is an element of {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 las 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 A(h+/-)(2, 1).