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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.00903 |
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| _version_ | 1866914620598386688 |
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| author | Chea, Vutha Vichea Vinet, Luc Zhedanov, Alexei |
| author_facet | Chea, Vutha Vichea Vinet, Luc Zhedanov, Alexei |
| contents | We identify the quadratic symmetry algebra of the two-dimensional Smorodinsky--Winternitz II system with a Laguerre-type confluent Heun algebra. The system is separable in Cartesian and parabolic coordinates. The complementary Cartesian separation operator \[
Y=\partial_y^2-ω^2y^2+\frac{1/4-c^2}{y^2} \] is of Laguerre type, while the parabolic integral \(W=L_2\) is its algebraic Heun partner. With \(Z=[Y,W]\), the defining relations are \[
[Y,Z]=16ω^2W-2bY,\qquad
[W,Z]=6Y^2-4HY+2bW+8ω^2(1-c^2), \] where \(H\) is central. This gives a direct superintegrable realization of the Laguerre--Heun algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00903 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The 2D Smorodinsky--Winternitz II system and the Laguerre--Heun algebra Chea, Vutha Vichea Vinet, Luc Zhedanov, Alexei Mathematical Physics 81R12 We identify the quadratic symmetry algebra of the two-dimensional Smorodinsky--Winternitz II system with a Laguerre-type confluent Heun algebra. The system is separable in Cartesian and parabolic coordinates. The complementary Cartesian separation operator \[ Y=\partial_y^2-ω^2y^2+\frac{1/4-c^2}{y^2} \] is of Laguerre type, while the parabolic integral \(W=L_2\) is its algebraic Heun partner. With \(Z=[Y,W]\), the defining relations are \[ [Y,Z]=16ω^2W-2bY,\qquad [W,Z]=6Y^2-4HY+2bW+8ω^2(1-c^2), \] where \(H\) is central. This gives a direct superintegrable realization of the Laguerre--Heun algebra. |
| title | The 2D Smorodinsky--Winternitz II system and the Laguerre--Heun algebra |
| topic | Mathematical Physics 81R12 |
| url | https://arxiv.org/abs/2606.00903 |