A core model for G 2

Abstract

The action of the affine Weyl group of type $A_n$ on its coroot lattice is classically modeled using $n$-cores, which are integer partitions with no hooks of length $n$. Exploiting an identification between the coroot lattices of types $G_2$ and $A_2$, we use $3$-cores to give a combinatorial model for the action of the affine Weyl group $\tilde{W}\left(G_2\right)$ on its coroot lattice.