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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorManocha, H.L.
dc.contributor.authorMiller, W., Jr.
dc.date.accessioned2008-10-30T03:02:40Z
dc.date.available2008-10-30T03:02:40Z
dc.date.issued1992-07
dc.identifier.citationKalnins, E.G., Manocha, H.L. & Miller, W., Jr. (1992). Models of q-algebra representations: Tensor products of special unitary and oscillator algebras. Journal of Mathematical Physics,33, 2365.en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1206
dc.description.abstractThis paper begins a study of one- and two-variable function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. The algebras considered are the quantum algebra Uq(su2) and a q analog of the oscillator algebra (not a quantum algebra). In each case a simple one-variable model of the positive discrete series of finite- and infinite-dimensional irreducible representations is used to compute the Clebsch–Gordan coefficients. It is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and the corresponding matrix elements of the ``group operators'' on these representation spaces are computed. It is shown that the matrix elements are polynomials satisfying orthogonality relations analogous to those holding for true irreducible group representations. It is also demonstrated that general q-hypergeometric functions can occur as basis functions in two-variable models, in contrast with the very restricted parameter values for the q-hypergeometric functions arising as matrix elements in the theory of quantum groups.en_US
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/33/2365/1en_US
dc.rightsCopyright 1992 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspen_US
dc.subjectMathematicsen_US
dc.subjectlie groupsen_US
dc.subjectirreducible representationsen_US
dc.subjecthypergeometric functionsen_US
dc.subjectClebsch&minusen_US
dc.subjectGordan coefficientsen_US
dc.subjectmatrix elementsen_US
dc.subjectlaguerre polynomialsen_US
dc.subjectanalytic functionsen_US
dc.subjecthilbert spaceen_US
dc.subjectoscillatorsen_US
dc.subjectunitarityen_US
dc.titleModels of q-algebra representations: Tensor products of special unitary and oscillator algebrasen_US
dc.typeJournal Articleen_US
dc.identifier.doi10.1063/1.529607en_US
dc.relation.isPartOfJournal of Mathematical Physicsen_NZ
pubs.begin-page2365en_NZ
pubs.elements-id84080
pubs.end-page2383en_NZ
pubs.issue7en_NZ
pubs.volume33en_NZ


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