PreprintCC BY 4.0HAL
Enumerating cores of charged multipartitions
Abstract
Granville and Ono proved that there is an e-core partition of n for every n ∈ N if and only if e ≥ 4, which translates to a statement about the existence of defect 0 blocks for symmetric groups in positive characteristic and defect 0 unipotent blocks of finite general linear groups in positive, non-defining characteristic. Motivated by analogous applications to the block theory of finite classical groups, imprimitive spetses, and cyclotomic Hecke algebras, we prove similar positivity statements about different variants of e-cores for charged multipartitions.
Related
BibTeX
@misc{gerber2026enumerating,
title = {{Enumerating cores of charged multipartitions}},
author = {Thomas Gerber and Emily Norton},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03738},
eprint = {2609.03738},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05788062v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Enumerating cores of charged multipartitions
AU - Thomas Gerber
AU - Emily Norton
PY - 2026
DA - 2026/09/03
PB - HAL
DO - 10.48550/arxiv.2609.03738
UR - https://hal.science/hal-05788062v1
AB - Granville and Ono proved that there is an e-core partition of n for every n ∈ N if and only if e ≥ 4, which translates to a statement about the existence of defect 0 blocks for symmetric groups in positive characteristic and defect 0 unipotent blocks of finite general linear groups in positive, non-defining characteristic. Motivated by analogous applications to the block theory of finite classical groups, imprimitive spetses, and cyclotomic Hecke algebras, we prove similar positivity statements about different variants of e-cores for charged multipartitions.
ER -