Non-commutative creation operators B̂_m are built for symmetric polynomials in matrix and Fock representations of W_{1+∞} and affine Yangian algebras.
Exact Solvability of the Calogero and Sutherland Models
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abstract
Translationally invariant symmetric polynomials as coordinates for $N$-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland $N$-body Hamiltonians, after appropriate gauge transformations, can be presented as a {\it quadratic} polynomial in the generators of the algebra $sl_N$ in finite-dimensional degenerate representation. The exact solvability of these models follows from the existence of the infinite flag of such representation spaces, preserved by the above Hamiltonians. A connection with Jack polynomials is discussed.
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2025 2verdicts
UNVERDICTED 2representative citing papers
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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Non-commutative creation operators for symmetric polynomials
Non-commutative creation operators B̂_m are built for symmetric polynomials in matrix and Fock representations of W_{1+∞} and affine Yangian algebras.
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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.