The duality in the affine actions on trees.

Abstract

Every action on a tree given by a (finite) automaton has an associated dual action given by the dual automaton. In this talk I will consider the affine groups of subrings of a global function field, construct their actions on a regular tree, and describe the dual action. In particular, this gives a natural family of bireversible automata and square complexes with interesting properties coming from the affine groups of global function fields. The talk is based on a joint work in progress with Dmytro Savchuk.