Related papers: Simply-laced isomonodromy systems
Explicit solutions to the Riemann-Hilbert problem will be found realising some irreducible non-rigid local systems. The relation to isomonodromy and the sixth Painleve equation will be described. Keywords: Riemann-Hilbert problem, Painleve…
We study walk algebras and Hecke algebras for Kac-Moody root systems. Each choice of orientation for the set of real roots gives rise to a corresponding "oriented" basis for each of these algebras. We show that the notion of distinguished…
In this paper we examine the bi-Hamiltonian structure of the generalized KdV-hierarchies. We verify that both Hamiltonian structures take the form of Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated system.…
In these lectures I consider the Hitchin integrable systems and their relations with the self-duality equations and the twisted super-symmetric Yang-Mills theory in four dimension follow Hitchin and Kapustin-Witten. I define the Symplectic…
In this paper we study root multiplicities of rank 2 hyperbolic Kac-Moody algebras using the combinatorics of Dyck paths.
We study a Hamiltonian system without the Painlev\'e property and show that it admits a kind of regularisation on a bundle of rational surfaces with certain divisors removed, generalising Okamoto's spaces of initial conditions for the…
The paper proposes an algorithm which could identify a general class of pdes describing dynamical systems with similar symmetries. The way that will be followed starts from a given group of symmetries, the determination of the invariants…
We consider the isomonodromy problems for flat $G$-bundles over punctured elliptic curves $\Sigma_\tau$ with regular singularities of connections at marked points. The bundles are classified by their characteristic classes. These classes…
Let G be a split real Kac-Moody group of arbitrary type and let K be its maximal compact subgroup, i.e. the subgroup of elements fixed by a Cartan-Chevalley involution of G. We construct non-trivial spin covers of K, thus confirming a…
Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…
We apply results from the geometry of nilpotent orbits and nilpotent Slodowy slices, together with modularity and asymptotic analysis of characters, to prove many new isomorphisms between affine W-algebras and affine Kac-Moody vertex…
In 1983, Feingold and Frenkel discovered a relation between Siegel modular forms of genus two and a rank-three hyperbolic Kac--Moody algebra extending the affine Lie algebra of type $A_1$. It inspires a problem to explore more general…
Wagoner complexes are simplicial complexes associated to groups of Kac-Moody type. They admit interesting homotopy groups which are related to integral group homology if the root datum is of 2-spherical type. We give a general definition of…
We give a criterion for a Dynkin diagram, equivalently a generalized Cartan matrix, to be symmetrizable. This criterion is easily checked on the Dynkin diagram. We obtain a simple proof that the maximal rank of a Dynkin diagram of compact…
In this paper the elliptic genus for a general Calabi-Yau fourfold is derived. The recent work of Kawai calculating N=2 heterotic string one-loop threshold corrections with a Wilson line turned on is extended to a similar computation where…
We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie…
We consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlev\'e equation. We establish an extended symmetry, complementing known results. The Calogero-Moser…
An overview is given on recent developments in the affine Weyl group approach to Painlev\'e equations and discrete Painlev\'e equations, based on the joint work with Y. Yamada and K. Kajiwara.
We make a generalization of the type C monomial space of a single variable, which was introduced in the construction of type C N-fold supersymmetry, to several variables. Then, we construct the most general quasi-solvable second-order…
For the affine and hyperbolic root system the symmetric part of the centralizers of root subgroups in the corresponding Steinberg groups are calculated. In the affine case the corresponding root subsystems can be computed in term of the…