Nonstandard GL_h(n) quantum groups and contraction of covariant q-bosonic algebras

Details Nonstandard GL_h(n) quantum groups and contraction of covariant q-bosonic algebras Nonstandard GL_h(n) quantum groups and contraction of covariant q-bosonic algebras

1998-10-28

arxiv.org/abs/math/9810161v1

Czech. J. Phys. 48 (1998) 1471-1476

Mathematics

Quantum Algebra

7 pages, LaTeX, no figure, presented at the 7th Colloquium ``Quantum Groups and Integrable Systems'', Prague, 18--20 June 1998

Scientific paper

$GL_h(n) \times GL_h(m)$-covariant $h$-bosonic algebras are built by contracting the $GL_q(n) \times GL_q(m)$-covariant $q$-bosonic algebras considered by the present author some years ago. Their defining relations are written in terms of the corresponding $R_h$-matrices. Whenever $n=2$, and $m=1$ or 2, it is proved by using U_h(sl(2)) Clebsch-Gordan coefficients that they can also be expressed in terms of coupled commutators in a way entirely similar to the classical case. Some U_h(sl(2)) rank-1/2 irreducible tensor operators, recently contructed by Aizawa in terms of standard bosonic operators, are shown to provide a realization of the $h$-bosonic algebra corresponding to $n=2$ and $m=1$.

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