Two variations on $(A_3\times A_1\times A_1)^{(1)}$ type discrete Painlev\'e equations

10 Apr 2019  ·  Shi Yang ·

By considering the normalizers of reflection subgroups of types $A_1^{(1)}$ and $A_3^{(1)}$ in $\widetilde{W}\left(D_5^{(1)}\right)$, two normalizers: $\widetilde{W}\left(A_3\times A_1\right)^{(1)}\ltimes {W}(A_1^{(1)})$ and $\widetilde{W}\left(A_1\times A_1\right)^{(1)}\ltimes {W}(A_3^{(1)})$ can be constructed from a $(A_{3}\times A_1\times A_1)^{(1)}$ type subroot system. These two symmetries arose in the studies of discrete \Pa equations \cite{KNY:2002, Takenawa:03, OS:18}, where certain non-translational elements of infinite order were shown to give rise to discrete \Pa equations... We clarify the nature of these elements in terms of Brink-Howlett theory of normalizers of Coxeter groups \cite{BH}. This is the first of a series of studies which investigates the properties of discrete integrable equations via the theory of normalizers. read more

PDF Abstract
No code implementations yet. Submit your code now

Categories


Mathematical Physics Mathematical Physics