Cohomologies of Affine Hyperelliptic Jacobi Varieties and Integrable Systems

Nakayashiki, Atsushi; Смирнов, Ф.

doi:10.1007/s002200100382

Cited by 30 publications

(85 citation statements)

References 8 publications

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“…In this section we briefly summarize necessary facts concerning relation between integrable models and algebraic geometry following the paper [2]. The reason for repeating certain facts from [2] is that we shall need them in slightly different situation.…”

Section: Affine Jacobianmentioning

confidence: 99%

“…The reason for repeating certain facts from [2] is that we shall need them in slightly different situation.…”

Section: Affine Jacobianmentioning

confidence: 99%

“…are counted by H g−1 [2]. The formula (6) can be useful only if we are able to control the cohomologies.…”

Section: Affine Jacobianmentioning

confidence: 99%

“…The formula (6) can be useful only if we are able to control the cohomologies. Concerning these cohomologies we adopt several conjectures following [2].…”

Section: Affine Jacobianmentioning

confidence: 99%

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Dual Baxter equations and quantization of the affine Jacobian

Смирнов¹

2000

J. Phys. A: Math. Gen.

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Abstract.A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the eigen-functions of its Hamiltonians coincide with the eigen-functions of Hamiltonians of the original model. We explain that this duality can be considered as duality between homologies and cohomologies of quantized affine hyper-elliptic Jacobian.0 Membre du CNRS 1 Laboratoire associé au CNRS.

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Section: Affine Jacobianmentioning

confidence: 99%

“…The reason for repeating certain facts from [2] is that we shall need them in slightly different situation.…”

Section: Affine Jacobianmentioning

confidence: 99%

See 2 more Smart Citations

Dual Baxter equations and quantization of the affine Jacobian

Смирнов¹

2000

J. Phys. A: Math. Gen.

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“…We use the same Poisson structure as used for the Mumford system [18,19]. This Poisson structure is defined on the 3g + 1-dimensional moduli space of the matrix V (λ) with coordinates α 1 , .…”

Section: Hamiltonian Structure Of Lax Equationsmentioning

confidence: 99%

Hamiltonian Structure of PI Hierarchy

Takasaki¹

2007

SIGMA

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Abstract. The string equation of type (2, 2g + 1) may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g > 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can be introduced in this hierarchy as well. The equations of motion in these Darboux coordinates turn out to take a Hamiltonian form, but the Hamiltonians are different from the Hamiltonians of the Lax equations (except for the lowest one that corresponds to the string equation itself).

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