Half-Diagrams in Partition Algebras: A Geometric Perspective on Multiplicities
Abstract
This paper studies the restriction multiplicities of half-diagram modules for the partition algebra and their geometric interpretations. By specializing the Bowman-De Visscher-Orellana formula [BVC, Theorem 4.3] for restriction multiplicities of standard modules in the partition algebra, we compute these multiplicities and provide interpretations in terms of planar triangles and conic sections. Additionally, through the decomposition of half-diagrams, we explain the intrinsic reasons underlying this connection between geometry and algebra.
Keywords
Cite
@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}
}
Comments
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