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 An 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 G2 and A2, we use 3-cores to give a combinatorial model for the action of the affine Weyl group W˜(G2) 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