17 citations · 24 across the 5 of their papers we have counts for
5 papers
Toward quantization of Galois theory
Akira Masuoka, Katsunori Saito, Hiroshi Umemura
This note is a development of our two previous papers, arXiv:1212.3392v1 and 1306.3660v1. The fundamental question is whether there exists a Galois theory, in which the Galois grou…
Toward quantized Picard-Vessiot theory, Further observations on our previous example
Katsunori Saito, Hiroshi Umemura
It is quite natural to wonder whether there is a difference-differential equations, the Galois group of which is a quantum group that is neither commutative nor co-commutative. Bel…
Can we quantize Galois theory ?
Katsunori Saito, Hiroshi Umemura
We present a non-linear difference-differential equation whoes Galois group is a non-commutative and non-co-comutative Hopf algebra.
Quantization of Galois theory, Examples and Observations
Katsunori Saito, Hiroshi Umemura
If we consider a q-analogue of linear differential equation, Galoois group of the q-analogue difference equation is still a linear algebraic group. Namely, by a quantization of lin…
Painlevé equations and deformations of rational surfaces with rational double points
Masa-Hiko Saito, Hiroshi Umemura
In this paper, we show that the Bäcklund transformations of Painlevé equations come from birational maps of rational surfaces constructed by Okamoto as the spaces of initial condit…