The quantum superalgebra $U_q[osp(1/2n)]$: deformed para-Bose operators and root of unity representations

Details The quantum superalgebra $U_q[osp(1/2n)]$: deformed para-Bose operators and root of unity representations The quantum superalgebra $U_q[osp(1/2n)]$: deformed para-Bose operators and root of unity representations

1995-01-16

arxiv.org/abs/q-alg/9501020v1

J.Phys. A28 (1995) 2605

Mathematics

Quantum Algebra

15 pages, LaTeX (latex twice), no figures

Scientific paper

10.1088/0305-4470/28/9/019

We recall the relation between the Lie superalgebra $osp(1/2n)$ and para-Bose operators. The quantum superalgebra $U_q[osp(1/2n)]$, defined as usual in terms of its Chevalley generators, is shown to be isomorphic to an associative algebra generated by so-called pre-oscillator operators satisfying a number of relations. From these relations, and the analogue with the non-deformed case, one can interpret these pre-oscillator operators as deformed para-Bose operators. Some consequences for $U_q[osp(1/2n)]$ (Cartan-Weyl basis, Poincar\'e-Birkhoff-Witt basis) and its Hopf subalgebra $U_q[gl(n)]$ are pointed out. Finally, using a realization in terms of ``$q$-commuting'' $q$-bosons, we construct an irreducible finite-dimensional unitary Fock representation of $U_q[osp(1/2n)]$ and its decomposition in terms of $U_q[gl(n)]$ representations when $q$ is a root of unity.

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