相关论文: Toda lattice and toric varieties for real split se…

This paper concerns the topology of isospectral real manifolds of certain Jacobi elements associated with real split semisimple Lie algebras. The manifolds are related to the compactified level sets of the generalized (nonperiodic) Toda…

This paper concerns the topology of the isospectral {\it real} manifold of the ${\mathfrak sl}(N)$ periodic Toda lattice consisting of $2^{N-1}$ different systems. The solutions of those systems contain blow-ups, and the set of those…

In this paper, we describe a connection that exists among (a) the number of singular points along the trajectory of Toda flow, (b) the cohomology of a compact subgroup $K$, and (c) the number of points of a Chevalley group $K({\mathbb…

The paper concerns a compactification of the isospectral varieties of nilpotent Toda lattices for real split simple Lie algebras. The compactification is obtained by taking the closure of unipotent group orbits in the flag manifolds. The…

Let $\sg$ be a complex finite-dimensional simple Lie algebra and let $\sg_l$ be the corresponding generalized Takiff algebra. This paper studies the affine variety $\ssf+\sb_l$ where $\ssf$ is similar to a principal nilpotent element of…

We study the isotropy representation of real flag manifolds associated to simple Lie algebras that are split real forms of complex simple Lie algebras. For each Dynkin diagram the invariant irreducible subspaces for the compact part of the…

We study the singularities (blow-ups) of the Toda lattice associated with a real split semisimple Lie algebra $\mathfrak g$. It turns out that the total number of blow-up points along trajectories of the Toda lattice is given by the number…

In this paper we continue our study of the geometric properties of full symmetric Toda systems from \cite{CSS14,CSS17,CSS19}. Namely we describe here a simple geometric construction of a commutative family of vector fields on compact…

The aim of this work is focused on linearizing and found the Lax Pairs of the algebraic complete integrability (a.c.i) Toda lattice associated with the twisted affine Lie algebra \(a_4^{\left(2\right)}\). Firstly, we recall that our case of…

We study the topology of the set of singular points (blow-ups) in the solution of the nonperiodic Toda lattice defined on real split semisimple Lie algebra $\mathfrak g$. The set of blow-ups is called the Painlev\'e divisor. The isospectral…

Let g be a semi-simple Lie algebra. In this paper we study the spaces of based quasi-maps from the projective line P^1 to the flag variety of g (it is well-known that their singularities are supposed to model the singularities of the so…

A totally nonnegative matrix is a real-valued matrix whose minors are all nonnegative. In this paper, we concern with the totally nonnegative structure of the finite Toda lattice, a classical integrable system, which is expressed as a…

We prove that any coadjoint orbit with real eigenvalues of a complex semisimple Lie group, equipped with the real part of the canonical holomorphic symplectic form, is symplectomorphic to the cotangent bundle of a (partial) flag manifold.…

For a simply connected (non-nilpotent) solvable Lie group $G$ with a lattice $\Gamma$ the de Rham and Dolbeault cohomologies of the solvmanifold $G/\Gamma$ are not in general isomorphic to the cohomologies of the Lie algebra $\mathfrak g$…

We classify solvable Lie groups admitting left invariant symplectic half-flat structure. When the Lie group has a compact quotient by a lattice, we show that these structures provide solutions of supersymmetric equations of type IIA.

A simply laced Dynkin diagram gives rise to a family of curves over $\mathbb{Q}$ and a coregular representation, using deformations of simple singularities and Vinberg theory respectively. Thorne has conjectured and partially proven a…

A set of two-dimensional semi-riemannian submanifolds of flat semi-riemannian manifolds is associated to each Toda theory. The method and an example are given to Toda theories associated to real finite dimensional Lie algebras.

The aim of this work is focused on the investigation of the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra $a_4^{(2)}$. First, we prove that the generic fiber of the momentum map for this…

We consider the iso-spectral real manifolds of tridiagonal Hessenberg matrices with real eigenvalues. The manifolds are described by the iso-spectral flows of indefinite Toda lattice equations introduced by the authors [Physica, 91D (1996),…

We prove that Ad-semisimple conjugacy classes in a connected Lie group $G$ are closed embedded submanifolds of $G$. We also prove that if $\alpha:H\to G$ is a homomorphism of connected Lie groups such that the kernel of $\alpha$ is discrete…