Abstract
In this article we present the q-analogue of results which were obtained in two earlier articles [1,2] for representations of the algebras su(2) and su(1, 1), including the unitarization of these representations. The carrier spaces for the representations of su(2) and su(1,1),which were discussed in [1,2], are Verma modules and certain subspaces and quotient spaces of Verma modules. The results obtained in [1,2] for su(2) and su(1, 1) are re-evaluated in the language of the q-calculus for corre-sponding quantum algebras su q (2) and su q (1,1) on “quantized” Verma modules (sections 2,3).
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References
B. Gruber, R. Lenczewski and M. Lorente, On induced scalar products and unitarization, J. Math. Phys. no. 3 31:587 (1990).
H.D. Doebner, B. Gruber and M. Lorente, Boson operator realizations of su(2) and su(1,1) and unitarization, J. Math. Phys. no. 3 30:594 (1989).
B. Gruber and A.U. Klimyk, Multiplicity free and finite multiplicity indecomposable representations of the algebra su(1,1), J. Math. Phys. no. 10 19:2009 (1978).
B. Gruber and A.U. Klimyk, Matrix elements for indecomposable representations of complex su(2), J. Math. Phys. no. 4 25:755 (1984).
D.B. Fairlie, q-Analysis and quantum groups, in “Symmetries in Science V”, this volume.
A.U. Klimyk, Yu.F. Smirnov and B. Gruber, Representations of the quantum algebras U q (su(2))and U q (su(1, 1)), in “Symmetries in Science V”, this volume.
Yu. F. Smirnov, V.N. Tolstoy and Yu.I. Kharitonov, Projection Operator Method and Q-Analog of Angular Momentum Theory, this volume.
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© 1991 Springer Science+Business Media New York
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Gruber, B., Smirnov, Y.F. (1991). On Quantized Verma Modules. In: Gruber, B., Biedenharn, L.C., Doebner, H.D. (eds) Symmetries in Science V. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3696-3_14
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DOI: https://doi.org/10.1007/978-1-4615-3696-3_14
Publisher Name: Springer, Boston, MA
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