文献类型：期刊文献

英文题名：HALF-DIAGRAMS IN PARTITION ALGEBRAS: A GEOMETRIC PERSPECTIVE ON MULTIPLICITIES

作者：Wang, Pei[1]; Zhuge, Changjing[2]

机构：[1] Teachers’ College, Beijing Union University, Beijing, 100101, China; [2] Beijing Institute for Scientific and Engineering Computing, Department of Mathematics, School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100124, China

第一机构：北京联合大学师范学院

年份：2025

外文期刊名：arXiv

收录：EI(收录号：20250507148)

语种：英文

外文关键词：Algebra - Computational geometry

摘要：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 [[BVC15], 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.MSC Codes 16D90, 16G10, 16E20 Copyright ? 2025, The Authors. All rights reserved.