A remark on Kac–Wakimoto hierarchies of D-type

@article{Wu2009ARO,
  title={A remark on Kac–Wakimoto hierarchies of D-type},
  author={Chao-Zhong Wu},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2009},
  volume={43},
  pages={035201}
}
  • Chao-Zhong Wu
  • Published 29 June 2009
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
For the Kac–Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D(1)n, we compute the coefficients of the corresponding Hirota bilinear equations, and verify the coincidence of these bilinear equations with the ones that are satisfied by Givental's total descendant potential of the Dn singularity, as conjectured by Givental and Milanov (2005 Simple singularities and integrable hierarchies The Breadth of Symplectic… 

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References

SHOWING 1-10 OF 57 REFERENCES

Simple singularities and integrable hierarchies

The paper [11] gives a construction of the total descendent potential corresponding to a semisimple Frobenius manifold. In [12], it is proved that the total descendent potential corresponding to K.

On the Drinfeld–Sokolov Hierarchies of D Type

We extend the notion of pseudo-differential operators that are used to represent the Gelfand–Dickey hierarchies and obtain a similar representation for the full Drinfeld–Sokolov hierarchies of D n

Generalized Drinfel'd-Sokolov hierarchies

A general approach is adopted to the construction of integrable hierarchies of partial differential equations. A series of hierarchies associated to untwisted Kac-Moody algebras, and conjugacy

Soliton equations, vertex operators, and simple singularities

We prove the equivalence of two hierarchies of soliton equations associated to a simply-laced finite Dynkin diagram. The first was defined by Kac and Wakimoto (Proc. Symp. Pure Math. 48:138–177,

Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the

A_{n-1} singularities and nKdV hierarchies

According to a conjecture of E. Witten proved by M. Kontsevich, a certain generating function for intersection indices on the Deligne -- Mumford moduli spaces of Riemann surfaces coincides with a

Transformation Groups for Soliton Equations —Euclidean Lie Algebras and Reduction of the KP Hierarchy—

This is the last chapter of our series of papers [1], [3], [10], [11] on transformation groups for soliton equations. In [1] a link between the KdV (Korteweg de Vries) equation and the affine Lie

The Witten equation, mirror symmetry and quantum singularity theory

For any non-degenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to the

KP Hierarchies of Orthogonal and Symplectic Type–Transformation Groups for Soliton Equations VI–

A series of new hierarchies of soliton equations are presented on the basis of the Kadomtsev-Petviashvili (KP) hierarchy. In contrast to the KP case, which admits GL( ∞) as its transformation group,

Lie algebras and equations of Korteweg-de Vries type

The survey contains a description of the connection between the infinite-dimensional Lie algebras of Kats-Moody and systems of differential equations generalizing the Korteweg-de Vries and
...