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

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dc.creatorQuesne, C.
dc.date1999-03-25
dc.date.accessioned2026-07-07T05:28:28Z
dc.date.available2026-07-07T05:28:28Z
dc.description$GL_h(n) \times GL_{h'}(m)$-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 ${\cal A}^{(α)}_{q\pm}(n,m)$, $α= 1, 2$. When using a basis of ${\cal A}^{(α)}_{q\pm}(n,m)$ 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 ${\cal A}_{h\pm}(2,1)$.
dc.descriptionLaTeX, uses amssym.sty, 24 pages, no figure, to be published in Int. J. Theor. Phys
dc.identifierhttps://arxiv.org/abs/math/9903151
dc.identifierhttp://arxiv.org/abs/math/9903151
dc.identifierInt.J.Theor.Phys. 38 (1999) 1905-1923
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78271
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleCovariant (hh')-Deformed Bosonic and Fermionic Algebras as Contraction Limits of q-Deformed Ones
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