Empty runner removal theorem for Ariki-Koike algebras
Representation Theory
2026-04-09 v2
Abstract
For the Iwahori-Hecke algebras of type , James and Mathas proved a theorem which relates -decomposition numbers for different values of , by adding empty runners to the James' abacus display. This result is often referred to as the empty runner removal theorem. In this paper, we extend this theorem to the Ariki-Koike algebras, establishing a similar relationship for the -decomposition numbers.
Cite
@article{arxiv.2506.08811,
title = {Empty runner removal theorem for Ariki-Koike algebras},
author = {Alice Dell'Arciprete and Lorenzo Putignano},
journal= {arXiv preprint arXiv:2506.08811},
year = {2026}
}
Comments
23 pages. arXiv admin note: substantial text overlap with arXiv:2310.08156; text overlap with arXiv:0908.1749 by other authors. v2: minor corrections, typos fixed, and an additional reference included