Related papers: The Sato Grassmannian and the CH hierarchy
We consider two embeddings between Grassmannians and study the associated morphisms between the corresponding Chow rings.
Topological Chern-Simons (CS) and BF theories and their holomorphic analogues are discussed in terms of de Rham and Dolbeault cohomologies. We show that Cech cohomology provides another useful description of the above topological and…
We construct the tri-Hamiltonian structure of the two-dimensional Toda hierarchy using the R-matrix theory.
The non-isospectral problem (Lax pair) associated with a hierarchy in 2+1 dimensions that generalizes the well known Camassa-Holm hierarchy is presented. Here, we have investigated the non-classical Lie symmetries of this Lax pair when the…
We study the cohomology theory of sheaf complexes for open embeddings of topological spaces and related subjects. The theory is situated in the intersection of the general Cech theory and the theory of derived categories. That is to say, on…
A map is presented that associates with each element of a loop group a solution of an equation related by a simple change of coordinates to the Camassa-Holm (CH) Equation. Certain simple automorphisms of the loop group give rise to Backlund…
We describe how the loop group maps corresponding to special submanifolds associated to integrable systems may be thought of as certain Grassmann submanifolds of infinite dimensional homogeneous spaces. In general, the associated families…
We provide a construction of the two-component Camassa-Holm (CH-2) hierarchy employing a new zero-curvature formalism and identify and describe in detail the isospectral set associated to all real-valued, smooth, and bounded…
We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge…
Algebraic and geometric structures associated with Birkhoff strata of Sato Grassmannian are analyzed. It is shown that each Birkhoff stratum $\Sigma_S$ contains a subset $W_{\hat{S}}$ of points for which each fiber of the corresponding…
The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised…
We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds…
We investigate in detail the topological gauged Wess-Zumino-Witten models describing topological Kazama-Suzuki models based on complex Grassmannians. We show that there is a topological sector in which the ring of observables (constructed…
This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar $CP^{n-1}$ and Grassmannian models. They naturally arise in the description of continuum limits of spin…
The relative Dolbeault cohomology which naturally comes up in the theory of Cech-Dolbeault cohomology turns out to be canonically isomorphic with the local (relative) cohomology of A. Grothendieck and M. Sato so that it provides a handy way…
Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral…
It this paper we present a new construction of a hamiltonian hierarchy associated to a cohomological field theory. We conjecture that in the semisimple case our hierarchy is related to the Dubrovin-Zhang hierarchy by a Miura transformation…
A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restricted Grassmannian are described, and a momentum map picture…
We study a Kadomtsev-Petviashvili system for the local Camassa-Holm hierarchy obtaining a candidate to the Baker-Akhiezer function for its first reduction generalizing the local Camassa-Holm. We focus our attention on the differences with…
We describe the geometrical ladder of equations for Abelian bundles and gerbes, as well as higher generalisations, in terms of the cohomology of an operator that combines de Rham and Cech cohomology.