Covariant (hh)-Deformed Bosonic and Fermionic Algebras as Contraction Limits of q-Deformed Ones

GLh(n) × GLh′(m)-covariant (hh)-bosonic (or (hh)-fermionic) algebras Ahh′±(n,m) are built in terms of the corresponding Rh and Rh′-matrices by contracting the GLq(n) × GLq±1(m)-covariant q-bosonic (or q-fermionic) algebras A q± (n,m), α = 1, 2. When using a basis of A q± (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 Uh(sl(2)) rank-1/2 irreducible tensor operators, recently constructed by Aizawa, are shown to provide a realization of Ah±(2, 1).