# DIS

## Seminar

### Irreducibility of q-Painlevé equation of type $A_6^{(1)}$ in the sense of order

Nishioka, S (Tokyo)
Wednesday 13 May 2009, 17:00-17:30

Satellite

#### Abstract

I introduce a result on the irreducibility of q-Painlevé equation of type $A_6^{(1)}$ in the sense of order using the notion of decomposable extensions. The equation is one of the special non-linear q-difference equations of order 2 with symmetry $(A_1+A_1)^{(1)}$ and is also called q-Painlevé equation of type II. The decomposable difference field extension is a difference analogue of K. Nishioka's which was defined to prove the irreducibility of the first Painlevé equation in the sense of Nishioka-Umemura. The strongly normal extension of difference fields defined by Bialynicki-Birula is decomposable. I proved that transcendental solutions of the equation in a decomposable extension may exist only for special parameters, and that all of them satisfies the identical well-known Riccati equation if we apply the Bäcklund transformations to it appropriate times.

#### Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.