Abstract: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 \[
Y=\partial_y^2-\omega^2y^2+\frac{1/4-c^2}{y^2} \] is of Laguerre type, while the parabolic integral \(W=L_2\) is its algebraic Heun partner. With \(Z=[Y,W]\), the defining relations are \[
[Y,Z]=16\omega^2W-2bY,\qquad
[W,Z]=6Y^2-4HY+2bW+8\omega^2(1-c^2), \] where \(H\) is central. This gives a direct superintegrable realization of the Laguerre--Heun algebra.
From: Luc Vinet [view email]
[v1]
Sat, 30 May 2026 21:57:22 UTC (9 KB)
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