تقرير
Racah algebras, the centralizer $Z_n(\mathfrak{sl}_2)$ and its Hilbert-Poincar\'e series
| العنوان: | Racah algebras, the centralizer $Z_n(\mathfrak{sl}_2)$ and its Hilbert-Poincar\'e series |
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| المؤلفون: | Crampe, Nicolas, Gaboriaud, Julien, d'Andecy, Loïc Poulain, Vinet, Luc |
| المصدر: | Ann. Henri Poincar\'e 23 (2022), no. 7, 2657--2682 |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematical Physics |
| الوصف: | The higher rank Racah algebra $R(n)$ introduced recently is recalled. A quotient of this algebra by central elements, which we call the special Racah algebra $sR(n)$, is then introduced. Using results from classical invariant theory, this $sR(n)$ algebra is shown to be isomorphic to the centralizer $Z_{n}(\mathfrak{sl}_2)$ of the diagonal embedding of $U(\mathfrak{sl}_2)$ in $U(\mathfrak{sl}_2)^{\otimes n}$. This leads to a first and novel presentation of the centralizer $Z_{n}(\mathfrak{sl}_2)$ in terms of generators and defining relations. An explicit formula of its Hilbert-Poincar\'e series is also obtained and studied. The extension of the results to the study of the special Askey-Wilson algebra and its higher rank generalizations is discussed. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s00023-021-01152-y |
| URL الوصول: | http://arxiv.org/abs/2105.01086 |
| رقم الأكسشن: | edsarx.2105.01086 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s00023-021-01152-y |
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