Related papers: ABJM Matrix Model and 2D Toda Lattice Hierarchy

The modular vector field plays an important role in the theory of Poisson manifolds and is intimately connected with the Poisson cohomology of the space. In this paper we investigate its significance in the theory of integrable systems. We…

We study the Hermitian supermatrix model involving an external source. We derive the determinantal formula for the supermatrix partition function, and also for the expectation value of the characteristic polynomial ratio, which yields the…

Searching for the integrable structures of supersymmetric gauge theories and topological strings, we study melting crystal, which is known as random plane partition, from the viewpoint of integrable systems. We show that a series of…

We introduce in this paper two dimensional lattice models whose continuum limit belongs to the $N=2$ series. The first kind of model is integrable and obtained through a geometrical reformulation, generalizing results known in the $k=1$…

In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. In this paper we construct other examples of integrable dynamics of Toda-type on the square lattice, as well as on the triangular lattice,…

Critical points of semiclassical expansions of solutions to the dispersionful Toda hierarchy are considered and a double scaling limit method of regularization is formulated. The analogues of the critical points characterized by the strong…

In our previous work \cite{LNS}, we constructed quasi-Casoratian solutions to the noncommutative $q$-difference two-dimensional Toda lattice ($q$-2DTL) equation by Darboux transformation, which we can prove produces the existing Casoratian…

We take the first step in extending the integrability approach to one-point functions in AdS/dCFT to higher loop orders. More precisely, we argue that the formula encoding all tree-level one-point functions of SU(2) operators in the defect…

The six-vertex model with domain wall boundary conditions (DWBC) on an N x N square lattice is considered. The two-point correlation function describing the probability of having two vertices in a given state at opposite (top and bottom)…

The Banach Poisson geometry of multi-diagonal Hamiltonian systems having infinitely many integrals in involution is studied. It is shown that these systems can be considered as generalizing the semi-infinite Toda lattice which is an example…

Consider a semi-infinite skew-symmetric moment matrix, $m_{\iy}$ evolving according to the vector fields $\pl m / \pl t_k=\Lb^k m+m \Lb^{\top k} ,$ where $\Lb$ is the shift matrix. Then the skew-Borel decomposition $ m_{\iy}:= Q^{-1} J…

In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. \ We first establish a criterion on the coprime-ness of two singular inner functions and…

Using a contraction procedure, we obtain Toda theories and their structures, from affine Toda theories and their corresponding structures. By structures, we mean the equation of motion, the classical Lax pair, the boundary term for half…

The squared eigenfunction symmetry for the Toda lattice hierarchy is explicitly constructed in the form of the Kronecker product of the vector eigenfunction and the vector adjoint eigenfunction, which can be viewed as the generating…

High rank solutions to the 2D Toda Lattice System are constructed simultaneously with the effective calculation of coefficients of the high rank commuting ordinary difference operators. Our technic is based on the study of discrete dynamics…

One of the most fascinating and technically demanding parts of the theory of two-dimensional integrable systems constitute the models with the spectral parameter on an elliptic curve, including Landau-Lifshitz and Krichever-Novikov…

This paper studies rational functions $\mathfrak{J}_\alpha(q)$, which depend on a positive element $\alpha$ of the root lattice of a root system. These functions arise as Shapovalov pairings of Whittaker vectors in Verma modules of highest…

Integrable lattice equations arising in the context of singular manifold equations for scalar, multicomponent KP hierarchies and 2D Toda lattice hierarchy are considered. These equation generate the corresponding continuous hierarchy of…

We associate bicomplexes with the finite Toda lattice and with a finite Toda field theory in such a way that conserved currents and charges are obtained by a simple iterative construction.

We introduce the sub-lattice approach, a procedure to generate, from a given integrable lattice, a sub-lattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point…