Models of q-algebra representations: Matrix elements of the q-oscillator algebra

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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.contributor.authorMukherjee, Sanchita
dc.date.accessioned2008-10-30T02:12:55Z
dc.date.available2008-10-30T02:12:55Z
dc.date.issued1993-11
dc.description.abstractThis article continues a study of function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. Here a q analog of the oscillator algebra (not a quantum algebra) is considered. 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. This ``local'' approach applies to more general families of special functions, e.g., with complex arguments and parameters, than does the quantum group approach. It is shown that the matrix elements themselves transform irreducibly under the action of the algebra. q analogs of a formula are found for the product of two hypergeometric functions 1F1 and the product of a 1F1 and a Bessel function. They are interpreted here as expansions of the matrix elements of a ``group operator'' (via the exponential mapping) in a tensor product basis (for the tensor product of two irreducible oscillator algebra representations) in terms of the matrix elements in a reduced basis. As a by-product of this analysis an interesting new orthonormal basis was found for a q analog of the Bargmann–Segal Hilbert space of entire functions.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.citationKalnins, E.G., Miller, W., Jr. & Mukherjee, S. (1993). Models of q-algebra representations: Matrix elements of the q-oscillator algebra. Journal of Mathematical Physics,34, 5333.en_US
dc.identifier.doi10.1063/1.530308en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1205
dc.language.isoen
dc.relation.isPartOfJournal of Mathematical Physicsen_NZ
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/34/5333/1en_US
dc.rightsCopyright 1993 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.subjectalgebrasen_US
dc.subjectlie groupsen_US
dc.subjectirreducible representationsen_US
dc.subjecthypergeometric functionsen_US
dc.subjectoscillatorsen_US
dc.subjectmatrix elementsen_US
dc.subjecthilbert spaceen_US
dc.subjectcommutation relationsen_US
dc.titleModels of q-algebra representations: Matrix elements of the q-oscillator algebraen_US
dc.typeJournal Articleen_US
pubs.begin-page5333en_NZ
pubs.elements-id84063
pubs.end-page5356en_NZ
pubs.issue11en_NZ
pubs.volume34en_NZ
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