Show simple item record  

dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.contributor.authorPost, Sarah
dc.date.accessioned2014-01-20T20:59:43Z
dc.date.available2014-01-20T20:59:43Z
dc.date.copyright2013-10-02
dc.date.issued2013
dc.identifier.citationKalnins, E. G., Miller, W., Jr. & Post, S. (2013). Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials. Symmetry, Integrability and Geometry: Methods and Applications, 9, 057.en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/8413
dc.description.abstractWe show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2) and so(3). By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.en_NZ
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.relation.urihttp://www.emis.de/journals/SIGMA/2013/057/en_NZ
dc.rights©2013 Copyright with the authors. This article is published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.en_NZ
dc.subjectAskey schemeen_NZ
dc.subjecthypergeometric orthogonal polynomialsen_NZ
dc.subjectquadratic algebrasen_NZ
dc.titleContractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomialsen_NZ
dc.typeJournal Articleen_NZ
dc.identifier.doi10.3842/SIGMA.2013.057en_NZ
dc.relation.isPartOfSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)en_NZ
pubs.begin-page1en_NZ
pubs.elements-id38907
pubs.end-page28en_NZ
pubs.issue057en_NZ
pubs.volume9en_NZ


Files in this item

This item appears in the following Collection(s)

Show simple item record