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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.contributor.authorPost, Sarah
dc.date.accessioned2011-07-17T22:10:31Z
dc.date.available2011-07-17T22:10:31Z
dc.date.issued2011
dc.identifier.citationKalnins, E.G., Miller, W. Jr & Post, S. (2011). Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 7, Article No. 051.en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/5484
dc.description.abstractWe show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials.en_NZ
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.relation.urihttp://www.emis.de/journals/SIGMA/2011/051/en_NZ
dc.rightsThis article has been published in the journal: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). © Copyright with the author.en_NZ
dc.subjectsuperintegrabilityen_NZ
dc.subjectquadratic algebrasen_NZ
dc.subjectmultivariable Wilson polynomialsen_NZ
dc.subjectmultivariable Racah polynomialsen_NZ
dc.titleTwo-variable Wilson polynomials and the generic superintegrable system on the 3-sphereen_NZ
dc.typeJournal Articleen_NZ
dc.identifier.doi10.3842/SIGMA.2011.051en_NZ
dc.relation.isPartOfSymmetry, Integrability and Geometry: Methods and Applicationsen_NZ
pubs.begin-page1en_NZ
pubs.elements-id36106
pubs.end-page26en_NZ
pubs.volume7 Article 51en_NZ


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