تقرير
On the Quantum Metaplectic Howe Duality
| العنوان: | On the Quantum Metaplectic Howe Duality |
|---|---|
| المؤلفون: | Brito, Matheus, De Martino, Marcelo |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Quantum Algebra, Mathematics - Representation Theory, 17B37, 20G42, 05E10 |
| الوصف: | We establish a quantum analogue of the classical metaplectic Howe duality involving the pair of Lie algebras $(\mathfrak{sp}_{2n},\mathfrak{sl}_2)$ in the case when $n=1$. Our results yield commuting representations of the pair of Drinfeld-Jimbo quantum groups $(\mathcal U_{q^2}(\mathfrak{sl}_2),\mathcal U_{q}(\mathfrak{sl}_2))$ realized in a suitable algebra of $q$-differential operators acting on the space of symplectic polynomial spinors. We obtain $q$-analogues for the symplectic Dirac operator, the Fischer decomposition, the expression for the symplectic polynomial monogenics and for the projection operators onto the monogenics. We also discuss $q$-analogues of generalized symmetries of the $q$-symplectic Dirac operator raising the homogeneous polynomial degree. Comment: 22 pages. Comments are welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.02205 |
| رقم الأكسشن: | edsarx.2407.02205 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |