Abstract
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 $q$-Painleve equation of type $A_4^{(1)}$. A determinant formula of Jacobi–Trudi type for a family of Laurent polynomials arising from the action of the Weyl group is also presented.
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