The Heun Equation and the Calogero-moser-sutherland System Iv: the Hermite-krichever Ansatz
نویسنده
چکیده
We develop a theory for the Hermite-Krichever Ansatz on the Heun equation. As a byproduct, we find formulae which reduce hyperelliptic integrals to elliptic ones.
منابع مشابه
The Heun Equation and the Calogero-moser-sutherland System I: the Bethe Ansatz Method
Olshanetsky and Perelomov proposed the family of integrable quantum systems, which is called the Calogero-Moser-Sutherland system or the Olshanetsky-Perelomov system ([5]). In early 90’s, Ochiai, Oshima and Sekiguchi classified the integrable models of quantum mechanics which are invariant under the action of a Weyl group with some assumption ([4]). For the BN (N ≥ 3) case, the generic model co...
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We obtain isomonodromic transformations for Heun’s equation by generalizing Darboux transformation, and we find pairs and triplets of Heun’s equation which have the same monodromy structure. By composing generalized Darboux transformations, we establish a new construction of the commuting operator which ensures finite-gap property. As an application, we prove conjectures in part III.
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We apply a method of perturbation for the BC1 Inozemtsev model from the trigonometric model and show the holomorphy of perturbation. Consequently, the convergence of eigenvalues and eigenfuncions which are expressed as formal power series is proved. We investigate also the relationship between L space and some finite dimensional space of elliptic functions.
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where ℘(x) is the Weierstrass ℘-function with periods (1, τ), ω0 = 0, ω1 = 1 2 , ω2 = − τ+1 2 , ω3 = τ 2 are half-periods, and li (i = 0, 1, 2, 3) are coupling constants. This model is a one-particle version of the BCN Inozemtsev system [6], which is known to be the universal quantum integrable system with BN symmetry [6, 11]. The BCN Calogero-Moser-Sutherland systems are special cases of BCN I...
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We justify the holomorphic perturbation for the 1particle Inozemtsev model from the trigonometric model and show the holomorphy of the eigenvalues and the eigenfuncions which are obtained by the series expansion. We investigate the relationship between the L 2 space and the nite dimensional space of certain elliptic functions, and determine the distribution of the \algebraic" eigenvalues on the...
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