paper

Empty runner removal theorem for Ariki-Koike algebras

arXiv:2506.08811 · doi:10.1016/j.jalgebra.2026.03.021

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.

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

Empty runner removal theorem for Ariki-Koike algebras · wovepaper