تقرير
The generalized Racah algebra as a commutant
| العنوان: | The generalized Racah algebra as a commutant |
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| المؤلفون: | Gaboriaud, Julien, Vinet, Luc, Vinet, Stéphane, Zhedanov, Alexei |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, 20C35, 22E70, 81R12 |
| الوصف: | The Racah algebra $R(n)$ of rank $(n-2)$ is obtained as the commutant of the \mbox{$\mathfrak{o}(2)^{\oplus n}$} subalgebra of $\mathfrak{o}(2n)$ in oscillator representations of the universal algebra of $\mathfrak{o}(2n)$. This result is shown to be related in a Howe duality context to the definition of $R(n)$ as the algebra of Casimir operators arising in recouplings of $n$ copies of $\mathfrak{su}(1,1)$. These observations provide a natural framework to carry out the derivation by dimensional reduction of the generic superintegrable model on the $(n-1)$ sphere which is invariant under $R(n)$. Comment: 7 pages, based on a talk given by Luc Vinet at the 32nd International Colloquium on Group Theoretical Methods in Physics (Group 32) |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1088/1742-6596/1194/1/012034 |
| URL الوصول: | http://arxiv.org/abs/1808.09518 |
| رقم الأكسشن: | edsarx.1808.09518 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1088/1742-6596/1194/1/012034 |
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