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Lame equation, sl(2) algebra and isospectral deformations

A V Turbiner 1989 J. Phys. A: Math. Gen. 22 L1-L3   doi: 10.1088/0305-4470/22/1/001  Help

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A V Turbiner
Inst. for Theor. & Exp. Phys., Moscow, USSR

Abstract. It is proven that the n-zone Lame equation is equivalent to a spectral problem for a quadratic element of a universal enveloping sl(2) algebra. The Riemannian surface corresponding to the eigenstates in a parametric space forms the (2n+1)-sheet surface which splits in four subsurfaces; three of them contain the same number of sheets.

Print publication: Issue 1 (7 January 1989)

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