The q-Higgs and Askey–Wilson algebras
A q-analogue of the Higgs algebra, which describes the symmetry properties of the harmonic oscillator on the 2-sphere, is obtained as the commutant of the oq1/2(2)⊕oq1/2(2) subalgebra of oq1/2(4) in the q-oscillator representation of the quantized universal enveloping algebra Uq(u(4)). This q-Higgs...
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2019-07-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S055032131930118X |
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doaj-708bd660de324138a6ae11a755f13edd2020-11-24T21:44:31ZengElsevierNuclear Physics B0550-32132019-07-01944The q-Higgs and Askey–Wilson algebrasLuc Frappat0Julien Gaboriaud1Eric Ragoucy2Luc Vinet3Laboratoire d'Annecy-le-Vieux de Physique Théorique LAPTh, BP 110 Annecy-le-Vieux, F-74941 Annecy Cedex, France; Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, F-74000 Annecy, FranceCentre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal (Québec), H3C 3J7, Canada; Corresponding author.Laboratoire d'Annecy-le-Vieux de Physique Théorique LAPTh, BP 110 Annecy-le-Vieux, F-74941 Annecy Cedex, France; Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, F-74000 Annecy, FranceCentre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal (Québec), H3C 3J7, CanadaA q-analogue of the Higgs algebra, which describes the symmetry properties of the harmonic oscillator on the 2-sphere, is obtained as the commutant of the oq1/2(2)⊕oq1/2(2) subalgebra of oq1/2(4) in the q-oscillator representation of the quantized universal enveloping algebra Uq(u(4)). This q-Higgs algebra is also found as a specialization of the Askey–Wilson algebra embedded in the tensor product Uq(su(1,1))⊗Uq(su(1,1)). The connection between these two approaches is established on the basis of the Howe duality of the pair (oq1/2(4),Uq(su(1,1))).http://www.sciencedirect.com/science/article/pii/S055032131930118X |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Luc Frappat Julien Gaboriaud Eric Ragoucy Luc Vinet |
| spellingShingle |
Luc Frappat Julien Gaboriaud Eric Ragoucy Luc Vinet The q-Higgs and Askey–Wilson algebras Nuclear Physics B |
| author_facet |
Luc Frappat Julien Gaboriaud Eric Ragoucy Luc Vinet |
| author_sort |
Luc Frappat |
| title |
The q-Higgs and Askey–Wilson algebras |
| title_short |
The q-Higgs and Askey–Wilson algebras |
| title_full |
The q-Higgs and Askey–Wilson algebras |
| title_fullStr |
The q-Higgs and Askey–Wilson algebras |
| title_full_unstemmed |
The q-Higgs and Askey–Wilson algebras |
| title_sort |
q-higgs and askey–wilson algebras |
| publisher |
Elsevier |
| series |
Nuclear Physics B |
| issn |
0550-3213 |
| publishDate |
2019-07-01 |
| description |
A q-analogue of the Higgs algebra, which describes the symmetry properties of the harmonic oscillator on the 2-sphere, is obtained as the commutant of the oq1/2(2)⊕oq1/2(2) subalgebra of oq1/2(4) in the q-oscillator representation of the quantized universal enveloping algebra Uq(u(4)). This q-Higgs algebra is also found as a specialization of the Askey–Wilson algebra embedded in the tensor product Uq(su(1,1))⊗Uq(su(1,1)). The connection between these two approaches is established on the basis of the Howe duality of the pair (oq1/2(4),Uq(su(1,1))). |
| url |
http://www.sciencedirect.com/science/article/pii/S055032131930118X |
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