In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a τ -function of the sixth Painlevé system by constructing an associated isomonodromic system within their theory of holonomic quantum fields. More recently an alternative isomonodromy theory was constructed based on bi-orthogonal polynomials on the unit circle with regular semi-cla...

Abstract An explicit description of the ring rational polynomials in r indeterminates as a representation Lie algebra endomorphisms k -th exterior power countably infinite-dimensional vector space is given. Our based on results by Laksov and Throup concerning symmetric structure polynomial ring. are approximate versions vertex operators occurring celebrated bosonic representation, due to Date, ...

We introduce a family of local deformations for meromorphic connections on P 1 in the neighborhood of a higher rank (simple) singularity. Following the scheme in Malgrange [16-18] we use these local models to prove that the zeros of the tau function , introduced by Jimbo, Miwa, and Ueno in their pioneering work on " Birkhoff " deformations at irregular singular points [12], occur at precisely t...

In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a τ -function of the sixth Painlevé system by constructing an associated isomonodromic system within their theory of holonomic quantum fields. More recently an alternative isomonodromy theory was constructed based on bi-orthogonal polynomials on the unit circle with regular semi-cla...

An explicit construction for Q-operators of the finite XXZ spin-chain with twisted boundary conditions is presented. The massless and the massive regime is considered as well as the root of unity case. It is explained how these results yield an alternative expression for the trace function employed in the description of the correlation functions of the inhomogeneous XXZ model on the infinite la...

A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3 + 1 dimensional KP, Jimbo–Miwa and BKP equations, thereby presenting their particular N-wave solutions. An opposite question is...

We extend similarity reductions of the coupled (2+1)-dimensional three-wave resonant interaction system to its Lax pair. Thus we obtain new 3× 3 matrix Fuchs–Garnier pairs for the third, fourth, and fifth Painlevé equations, together with the previously known Fuchs–Garnier pair for the sixth Painlevé equation. These Fuchs–Garnier pairs have an important feature: they are linear with respect to ...

We analyze isomonodromic deformations of rational connections on the Riemann sphere with Fuchsian and irregular singularities. The Fuchsian singularities are allowed to be of arbitrary resonant index; the irregular singularities are also allowed to be resonant in the sense that the leading coefficient matrix at each singularity may have arbitrary Jordan canonical form, with a genericity conditi...