Abacus models for parabolic quotients of affine Weyl groups

TL;DR

This paper introduces abacus diagrams and combinatorial models for minimal length coset representatives in affine Weyl groups of types B, C, and D, extending classical affine type A results.

Contribution

It generalizes abacus diagrams and combinatorial models to affine Weyl groups of types B, C, and D, building on Eriksson's realization of type C.

Findings

Abacus diagrams for types B, C, D constructed

Generalization of classical affine type A results

Connections to core partitions established

Abstract

We introduce abacus diagrams that describe minimal length coset representatives in affine Weyl groups of types B, C, and D. These abacus diagrams use a realization of the affine Weyl group of type C due to Eriksson to generalize a construction of James for the symmetric group. We also describe several combinatorial models for these parabolic quotients that generalize classical results in affine type A related to core partitions.