A core model for G2

Cotton, Benjamin; Williams, Nathan F.

doi:10.2140/involve.2021.14.401

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A core model for $G_2$

Benjamin Cotton and Nathan F. Williams

Vol. 14 (2021), No. 3, 401–412

DOI: 10.2140/involve.2021.14.401

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 $\tilde{W} (G_{2})$ on its coroot lattice.

Keywords

partitions, cores, affine Weyl group, affine symmetric group, coroot

Mathematical Subject Classification

Primary: 05E10

Milestones

Received: 12 June 2020

Revised: 9 February 2021

Accepted: 10 February 2021

Published: 17 July 2021

Communicated by Jim Haglund

Authors

Benjamin Cotton
Department of Mathematical Sciences University of Texas at Dallas Richardson, TX United States

Nathan F. Williams
Department of Mathematical Sciences University of Texas at Dallas Richardson, TX United States

Vol. 14, No. 3, 2021