Conjectures that for integer k the TTW Hamiltonian H and integrals I1, I2, I12 generate a polynomial algebra of order k+1 inside hidden algebra g^(k), verified explicitly for k=1 to 4.
Post, Models of Quadratic Algebras Generated by Superintegrable Systems in 2D, SIGMA7, 036 (2011) (20 pp.)
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Review confirms exact solvability, algebraic forms, hidden Lie algebras, and polynomial integral algebras for six 2D superintegrable systems including Smorodinsky-Winternitz, Fokas-Lagerstrom, Calogero-Wolfes, and TTW models.
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Tremblay-Turbiner-Winternitz (TTW) system at integer index $k$: polynomial algebras of integrals
Conjectures that for integer k the TTW Hamiltonian H and integrals I1, I2, I12 generate a polynomial algebra of order k+1 inside hidden algebra g^(k), verified explicitly for k=1 to 4.
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Quantum two-dimensional superintegrable systems in flat space: exact-solvability, hidden algebra, polynomial algebra of integrals
Review confirms exact solvability, algebraic forms, hidden Lie algebras, and polynomial integral algebras for six 2D superintegrable systems including Smorodinsky-Winternitz, Fokas-Lagerstrom, Calogero-Wolfes, and TTW models.