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Main Authors: Xiang, Shang, Feng, Hao, Zhuo, Keyou, Chen, Tian-Shun, Zhang, Kilar
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2512.07758
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author Xiang, Shang
Feng, Hao
Zhuo, Keyou
Chen, Tian-Shun
Zhang, Kilar
author_facet Xiang, Shang
Feng, Hao
Zhuo, Keyou
Chen, Tian-Shun
Zhang, Kilar
contents To construct a BPS algebra with representations furnished by n-dimensional partitions, the first step is to find the eigenvalues of the Cartan operators acting on them. The generating function of the eigenvalues is called the charge function. It has an important property that for each partition, the poles of the function correspond to the projection of the boxes which can be added to or removed from the partition legally. The charge functions of lower dimensional partitions, i.e., Young diagrams for 2D, plane partitions for 3D and solid partitions for 4D, are already given in the literature. In this paper, we propose an expression of the charge function for arbitrary odd dimensional partitions and have it proved for 5D case. Some explicit numerical tests for 7D and 9D case are also conducted to confirm our formula.
format Preprint
id arxiv_https___arxiv_org_abs_2512_07758
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Charge functions for odd dimensional partitions
Xiang, Shang
Feng, Hao
Zhuo, Keyou
Chen, Tian-Shun
Zhang, Kilar
Mathematical Physics
High Energy Physics - Theory
To construct a BPS algebra with representations furnished by n-dimensional partitions, the first step is to find the eigenvalues of the Cartan operators acting on them. The generating function of the eigenvalues is called the charge function. It has an important property that for each partition, the poles of the function correspond to the projection of the boxes which can be added to or removed from the partition legally. The charge functions of lower dimensional partitions, i.e., Young diagrams for 2D, plane partitions for 3D and solid partitions for 4D, are already given in the literature. In this paper, we propose an expression of the charge function for arbitrary odd dimensional partitions and have it proved for 5D case. Some explicit numerical tests for 7D and 9D case are also conducted to confirm our formula.
title Charge functions for odd dimensional partitions
topic Mathematical Physics
High Energy Physics - Theory
url https://arxiv.org/abs/2512.07758