带电多重分拆的核枚举
Enumerating cores of charged multipartitions
- Université Claude Bernard Lyon 1（里昂第一大学）
- University of Kent（肯特大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文围绕带电多重分拆的不同e-核变体，证明了类似Granville与Ono关于e-核分拆存在性的正性命题，为相关群与代数的块理论应用提供支撑。
AI中文摘要：
Granville与Ono证明，当且仅当e≥4时，对所有自然数n都存在n的e-核分拆，这一结论对应正特征下对称群亏格0块及正非定义特征下有限一般线性群亏格0幂幺块的存在性命题。受有限典型群块理论、非本原spetses及分圆Hecke代数类似应用的驱动，我们针对带电多重分拆的不同e-核变体，证明了类似的正性命题。
英文摘要：
Granville and Ono proved that there is an $e$-core partition of $n$ for every $n\in\mathbb{N}$ if and only if $e\geq 4$, 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.
