Abstract
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the “projectivized” representation possessing an invariant subspace and the spectral problem for a certain linear differential operator. As examples, some polynomials connected to sl 2(R), sl 2(R)q,osp(2, 2) and so 3 are briefly discussed.
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Turbiner, A. (1993). Lie Algebras and Polynomial Solutions of Differential Equations. In: Osborn, H. (eds) Low-Dimensional Topology and Quantum Field Theory. NATO ASI Series, vol 315. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1612-9_27
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DOI: https://doi.org/10.1007/978-1-4899-1612-9_27
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