University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Irreducibility of q-Painlev equation of type $A_6^{(1)}$ in the sense of order

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

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Discrete Integrable Systems

I introduce a result on the irreducibility of q-Painlev equation of type $A_6$ 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-Painlev 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 Painlev 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 Bcklund transformations to it appropriate times.

This talk is part of the Isaac Newton Institute Seminar Series series.

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