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Raising and lowering operators for uq(n)

par Quesne, Christiane
Référence Journal of Physics A: Mathematical and General, 26, 2, page (357-372), 020
Publication Publié, 1993

Article révisé par les pairs

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Résumé :

After reviewing the defining relations for the gq-algebra uq(n), the author constructs a Cartan-Weyl basis and lists the q-commutation relations of its generators. He then uses the latter to explicitly construct sets of raising and lowering operators for the canonical chain of q-algebras u q(n)uq(n-1), generalizing those introduced by Nagel and Moshinsky (1965) for u(m)u(n-1). Finally, he gives their normalization coefficients and shows how the normalized operators can be used to go from any Gel'fand-Tseitlin basis state that is of highest weight in uq(n-1) to any other one and ultimately to construct the whole Gel'fand-Tseitlin basis from its highest-weight state. This work both generalizes a previous work of Ueno et al. (1989) on lowering operators and provides explicit expressions for their operators in terms of uq(n) Cartan-Weyl generators.