Related papers: Polynomial Toda maps are transfer matrices
We discuss several constructions of swap polynomials, that is 2--tensor valued matrix polynomials which are multiples of the swap or switch operator.
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 show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same property. The construction of the correspond- ing family of matrix…
Toda equations associated with twisted loop groups are considered. Such equations are specified by Z-gradations of the corresponding twisted loop Lie algebras. The classification of Toda equations related to twisted loop Lie algebras with…
Using the procedure of the marked point fusion, there are obtained integrable systems with poles in the matrix of the Lax operator order higher than one, considered Hamiltonians, symplectic structure and symmetries of these systems. Also,…
We show that Toda lattices with the exceptional Cartan matrices are Liouville type systems. For these systems of equations, we obtain explicit formulas for the invariants and generalized Laplace invariants.
Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea…
On the set of mappings of the given set, we define the product of mappings. If A is associative algebra, then we consider the set of matrices, whose elements are linear mappings of algebra A. In algebra of matrices of linear mappings we…
In this paper, we study transfer functions corresponding to parametric linear systems whose coefficients are block matrices. Thus, these transfer functions constitute Laurent polynomials whose coefficients are square matrices. We assume…
We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…
Inspired by a well-known characterization of the index of an inclusion of II$_1$ factors due to Pimsner and Popa, we define an index-type invariant for inclusions of operator systems. We compute examples of this invariant, show that it is…
We present a method for calculating transfer matrices for the $q$-state Potts model partition functions $Z(G,q,v)$, for arbitrary $q$ and temperature variable $v$, on strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc)…
Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix with entries in a ring of noncommutative Laurent polynomials with integer coefficients. We show that such a zeta function is an algebraic…
This paper addresses the issue of integrable structure in a modified melting crystal model of topological string theory on the resolved conifold. The partition function can be expressed as the vacuum expectation value of an operator on the…
The superintegrability of the non-periodic Toda lattice is explained in the framework of systems written in action-angles coordinates. Moreover, a simpler form of the first integrals is given.
In this paper, the classification in [Lin,Wei,Ye] of solutions to Toda systems of type $A$ with singular sources is generalized to Toda systems of types $C$ and $B$. Like in the $A$ case, the solution space is shown to be parametrized by…
In this paper, autonomous differential equations type delta of order one on integral domains are defined. For this we will use the autonomous ring defined on the Hurwitz expansion ring of exponential generating functions with coefficients…
Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry…
A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two ``coupling'' matrices and is sufficiently general to include all Toda field theories existing in the literature. Lie point…
Some new developments in constrained Lax integrable systems and their applications to physics are reviewed. After summarizing the tau function construction of the KP hierarchy and the basic concepts of the symmetry of nonlinear equations,…