划分代数中的半图：重数的几何视角
表示论
2025-11-11 v1 组合数学
摘要
本文研究了划分代数中半图模的限制重数及其几何解释。通过将Bowman-De Visscher-Orellana关于划分代数中标准模限制重数的公式[BVC, Theorem 4.3]进行特化，我们计算了这些重数，并从平面三角形和圆锥曲线的角度提供了解释。此外，通过半图的分解，我们解释了几何与代数之间这种联系的内在原因。
引用
@article{arxiv.2511.06258,
title = {Half-Diagrams in Partition Algebras: A Geometric Perspective on Multiplicities},
author = {Pei Wang and Changjing Zhuge},
journal= {arXiv preprint arXiv:2511.06258},
year = {2025}
}
备注
Comments are welcome. The authors wish to express their sincere gratitude to colleagues for their constructive comments during the development of this manuscript. Their valuable suggestions have significantly enhanced the quality of this work