PreprintCC BY-NC-SA 4.0arXiv
New runner removal theorems for the cyclotomic Hecke algebras of type G(r,1,n)
Abstract
For the Iwahori-Hecke algebras ℋq(Sn) of the symmetric group Sn at a primitive e-th root of unity, James and Mathas proved a theorem which relates v-decomposition numbers dλμe(v) for different values of e, by adding ``empty runners'' to the abacus display for the labelling partitions λ,μ. Fayers proved a similar theorem, which involves adding ``full'' runners to these abacus displays. In this paper we use Uglov's map from the set of r-abaci for r-partitions to the set of e-abaci for partitions to extend these theorems to the cyclotomic Hecke algebras of type G(r,1,n).
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BibTeX
@misc{hu2026runner,
title = {{New runner removal theorems for the cyclotomic Hecke algebras of type $G(r,1,n)$}},
author = {Jun Hu and Xiangyu Qi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15115},
eprint = {2609.15115},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15115},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - New runner removal theorems for the cyclotomic Hecke algebras of type G(r,1,n)
AU - Jun Hu
AU - Xiangyu Qi
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.15115
UR - https://arxiv.org/abs/2609.15115
AB - For the Iwahori-Hecke algebras ℋ_q(S_n) of the symmetric group S_n at a primitive e-th root of unity, James and Mathas proved a theorem which relates v-decomposition numbers d_λμ^e(v) for different values of e, by adding ``empty runners'' to the abacus display for the labelling partitions λ,μ. Fayers proved a similar theorem, which involves adding ``full'' runners to these abacus displays. In this paper we use Uglov's map from the set of r-abaci for r-partitions to the set of e-abaci for partitions to extend these theorems to the cyclotomic Hecke algebras of type G(r,1,n).
ER -