The Heun Equation and the Calogero-Moser-Sutherland System IV: The Hermite-Krichever Ansatz
نویسندگان
چکیده
منابع مشابه
The Heun Equation and the Calogero-moser-sutherland System Iv: the Hermite-krichever Ansatz
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.
متن کاملThe 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...
متن کاملThe Heun Equation and the Calogero-moser-sutherland System Ii: the Perturbation and the Algebraic Solution
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...
متن کاملThe Heun Equation and the Calogero-moser-sutherland System Ii: Perturbation and Algebraic Solution
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.
متن کاملThe Heun Equation and the Calogero-moser-sutherland System V: Generalized Darboux Transformations
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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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2005
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-005-1359-9