Related papers: Variations of $q$-Garnier system
We give a simple form of the evolution equation and a scalar Lax pair for the $q$-Garnier system. Some reductions to the $q$-Painlev\'e equations and the autonomous case as a generalized QRT system are discussed. Using two kinds of Pad\'e…
The $q$-Garnier system was first proposed by Sakai and its other directions of discrete time evolutions were given by Nagao and Yamada. Recently, it was shown that all of those directions of discrete time evolutions are derived from a…
Recently a certain $q$-Painlev\'e type system has been obtained from a reduction of the $q$-Garnier system. In this paper it is shown that the $q$-Painlev\'e type system is associated with another realization of the affine Weyl group…
We derive a $q$-analogue of the matrix sixth Painlev\'e system via a connection-preserving deformation of a certain Fuchsian linear $q$-difference system. In specifying the linear $q$-difference system, we utilize the correspondence between…
We investigate the symmetry of the linear q-difference equations which are associated with some q-Painlev\'e equations. We apply it for adjustment of the expression of the time evolution on the q-Painlev\'e equations in terms of the Weyl…
We study some Hamiltonian structures of the Garnier system in two variables from the viewpoints of its symmetry and holomorphy properties. We also give a generalization of {\it Okamoto transformation \it}of the sixth Painlev\'e system.
A system of q-Painlev\'e type equations with multi-time variables t_1,...,t_M is obtained as a similarity reduction of the N-reduced q-KP hierarchy. This system has affine Weyl group symmetry of type A^{(1)}_{M-1} \times A^{(1)}_{N-1}. Its…
We construct and characterize quantum Garnier systems in two variables including degenerate cases by certain holomorphic properties under the quantum canonical transformations.
In this article we formulate a group of birational transformations which is isomorphic to an extended affine Weyl group of type $(A_{2n+1}+A_1+A_1)^{(1)}$ with the aid of mutations and permutations of vertices to a mutation-periodic quiver…
We study the degenerate Garnier system which generalizes the fifth Painlev\'{e} equation. We present two classes of particular solutions, classical transcendental and algebraic ones. Their coalescence structure is also investigated.
We present {\it symmetric Hamiltonians} for the degenerate Garnier systems in two variables. For these symmetric Hamiltonians, we make the symmetry and holomorphy conditions, and we also make a generalization of these systems involving…
We consider a degeneration of the $q$-matrix sixth Painlev\'e system. As a result, we obtain a system of non-linear $q$-difference equations, which describes a deformation of a certain non-Fuchsian linear $q$-difference system. We define…
We derive integrable discrete systems which are contiguity relations of two equations in the Painlev\'e-Gambier classification depending on some parameter. These studies extend earlier work where the contiguity relations for the six…
Relations between differential calculi, quantum groups, integrable systems, and q-analysis are studied. Some new Hirota type formulas are established for qKP along with variations on classical Hirota formulas.
In this note, we will compare the Garnier system in two variables with four-dimensional partial differential system in two variables with $W(D_6^{(1)})$-symmetry. Both systems are different in each compactification in the variables…
We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by…
We study movable singularities of Garnier systems using the connection of the latter with Schlesinger isomonodromic deformations of Fuchsian systems
The diagonal spin-spin correlations $ \langle \sigma_{0,0}\sigma_{N,N} \rangle $ of the Ising model on a triangular lattice with general couplings in the three directions are evaluated in terms of a solution to a three-variable extension of…
Considering a certain interpolation problem, we derive a series of elliptic difference isomonodromic systems together with their Lax forms. These systems give a multivariate extension of the elliptic Painlev\'e equation.
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…