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arXiv · 2506.08811

Empty runner removal theorem for Ariki-Koike algebras

Alice Dell'Arciprete·Lorenzo Putignano
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Abstract

For the Iwahori-Hecke algebras of type $A$, James and Mathas proved a theorem which relates $v$-decomposition numbers for different values of $e$, 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 $v$-decomposition numbers.

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BibTeXRIS

Alice Dell'Arciprete, Lorenzo Putignano. 2025-06-10. Empty runner removal theorem for Ariki-Koike algebras. https://doi.org/10.1016/j.jalgebra.2026.03.021

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