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The q-Higgs and Askey–Wilson algebras
oleh: Luc Frappat, Julien Gaboriaud, Eric Ragoucy, Luc Vinet
Format: | Article |
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Diterbitkan: | Elsevier 2019-07-01 |
Deskripsi
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))).