Year: 2026
Type: preprint
Abstract: For the Iwahori-Hecke algebras $\mathcal H_q(\mathfrak S_n)$ of the symmetric group $\mathfrak S_n$ 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 $G(r,1,n)$.
Source: arXiv (Cornell University)
Authors: Hu, Jun, Qi, Xiangyu
Institution: Beijing Institute of Technology
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4926649899
OpenAlex ID: W7213285246