Iterated monodromy groups of Chebyshev-like maps on $\mathbb{C}^n$

TL;DR

This paper explores the connection between affine Weyl groups and Chebyshev-like polynomial maps on complex n-space, revealing that each affine Weyl group can be realized as an iterated monodromy group of such maps.

Contribution

It establishes a novel correspondence between affine Weyl groups and Chebyshev-like maps, expanding understanding of their algebraic and dynamical properties.

Findings

Affine Weyl groups appear as iterated monodromy groups of certain polynomial maps.

Each affine Weyl group can be realized through a Chebyshev-like polynomial self-map on ^n.

The work links algebraic group theory with complex dynamical systems.

Abstract

Every affine Weyl group appears as the iterated monodromy group of a Chebyshev-like polynomial self-map of $\mathbb{C}^n$.