Dimer models with group actions

A dimer model is a graph embedded in the real two torus whose nodes are colored black or white, which satisfies a certain condition. A dimer model determines a lattice polygon called the characteristic polygon. If a dimer model is "consistent", then it describes (commutative or non-commutative) crepant resolutions of Gorenstein affine toric 3-fold associated with the characteristic polygon. In this talk, we consider the relation between dimer models with finite group action and crepant resolutions of finite quotients of Gorenstein affine toric 3-folds. Further we discuss the existence of consistent dimer models for a given lattice polygon with a finite group action. This is a joint work with Kazushi Ueda and Alvaro Nolla de Celis.