#### Vol. 14, No. 3, 2021

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A core model for $G_2$

### Benjamin Cotton and Nathan F. Williams

Vol. 14 (2021), No. 3, 401–412
##### 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 $\stackrel{˜}{W}\left({G}_{2}\right)$ on its coroot lattice.

##### Keywords
partitions, cores, affine Weyl group, affine symmetric group, coroot
Primary: 05E10