GLh(n) ×GLh′(m)-covariant (hh′)-bosonic[or (hh′)-fermionic] algebras \documentclass[12pt]{minimal}
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$$\mathcal{A}_{hh' \pm } \left( {n,m} \right)$$
\end{document} are built in terms of thecorresponding Rh and\documentclass[12pt]{minimal}
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$$R_{h'}$$
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$${\text{GL}}_{q^{ \pm 1} } \left( m \right)$$
\end{document}-covariant q-bosonic (or q-fermionic) algebras \documentclass[12pt]{minimal}
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$$\mathcal{A}_{_{q \pm } }^{\left( {\alpha } \right)} \left( {n,m} \right)$$
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$$\mathcal{A}_{_{q \pm } }^{\left( {\alpha } \right)} \left( {n,m} \right)$$
\end{document} wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra Uq(gl(n)) ⊗ \documentclass[12pt]{minimal}
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$${\text{U}}_{q^{ \pm 1} } \left( {{\text{gl}}\left( m \right)} \right)$$
\end{document}, a contraction limit only exists forn, m ∈ {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingUh(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some Uh(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of \documentclass[12pt]{minimal}
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$$\mathcal{A}_{_{h \pm } } $$
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