The dual pair (Uq(su(1,1)),oq1/2(2n)), <i>q</i>-oscillators, and Askey-Wilson algebras
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Bibliographic record
Abstract
The universal Askey–Wilson algebra AW(3) can be obtained as the commutant of Uq(su(1,1)) in Uq(su(1,1))⊗3. We analyze the commutant of oq1/2(2)⊕oq1/2(2)⊕oq1/2(2) in q-oscillator representations of oq1/2(6) and show that it also realizes AW(3). These two pictures of AW(3) are shown to be dual in the sense of Howe; this is made clear by highlighting the role of the intermediate Casimir elements of each member of the dual pair Uq(su(1,1)),oq1/2(6). We also generalize these results. A higher rank extension of the Askey–Wilson algebra denoted AW(n) can be defined as the commutant of Uq(su(1,1)) in Uq(su(1,1))⊗n, and a dual description of AW(n) as the commutant of oq1/2(2)⊕n in q-oscillator representations of oq1/2(2n) is offered by calling upon the dual pair Uq(su(1,1)),oq1/2(2n).
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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