Cuspidal ribbon tableaux in affine type A

DOI

10.5802/alco.260

Authors

Dina Abbasian, Washington & Jefferson College
Lena Difulvio, Washington & Jefferson College
Robert Muth, Duquesne University
Gabrielle Pasternak, Washington & Jefferson College
Isabella Sholtes, Washington & Jefferson College
Frances Sinclair, Washington & Jefferson College

Document Type

Journal Article

Publication Date

1-1-2023

Publication Title

Algebraic Combinatorics

Volume

6

Issue

2

First Page

285

Last Page

319

Keywords

Khovanov-Lauda-Rouquier algebras, quiver Hecke algebras, ribbon tableaux, Specht modules, Young diagrams

Abstract

For any convex preorder on the set of positive roots of affine type A, we classify and construct all associated cuspidal and semicuspidal skew shapes. These combinatorial objects correspond to cuspidal and semicuspidal skew Specht modules for the Khovanov-Lauda-Rouquier algebra of affine type A. Cuspidal skew shapes are ribbons, and we show that every skew shape has a unique ordered tiling by cuspidal ribbons. This tiling data provides an upper bound, in the bilexicographic order on Kostant partitions, for labels of simple factors of Specht modules.

Open Access

Gold

Repository Citation

Abbasian, D., Difulvio, L., Muth, R., Pasternak, G., Sholtes, I., & Sinclair, F. (2023). Cuspidal ribbon tableaux in affine type A. Algebraic Combinatorics, 6 (2), 285-319. https://doi.org/10.5802/alco.260