Polynomial deformations of sl(2,R) in a three-dimensional invariant subspace of monomials

Abstract

New finite-dimensional representations of specific polynomial deformations of sl(2,R) are constructed. The corresponding generators can be, in particular, realized through linear differential operators preserving a finite-dimensional subspace of monomials. We concentrate on three-dimensional spaces.

References in corpus (2)

• Classification of linear differential operators with an invariant subspace of monomials
• On the relation between polynomial deformations of sl(2,R) and quasi-exactly solvability

Cited by in corpus (4)

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• Generalized rotational hamiltonians from nonlinear angular momentum algebras
• Polynomial algebras from Lie algebra reduction chains $\mathfrak{g}\supset {\mathfrak{g}}^{\prime }$
• Generalized quantum Zernike Hamiltonians: Polynomial Higgs-type algebras and algebraic derivation of the spectrum