Aq-deformation of discrete dynamical systems associated with the Weyl group of typeA

A |q|-deformation of discrete dynamical systems associated with the Weyl group of type |A| is proposed. This is a natural generalization of the birational Weyl group action for the |q|-Painlevé equation of type |A₄⁽¹⁾|⁠. A determinant formula of Jacobi–Trudi type for a family of Laurent polynomials arising from the action of the Weyl group is also presented. Communicated by: Prof.