Branching rules for cell modules on a tower of the partition algebras
Representation Theory
2025-11-12 v2 Quantum Algebra
Rings and Algebras
Abstract
Partition algebras with non-zero parameters are cellularly stratified and thus have the features of both cellular algebras and stratified algebras. Also, partition algebras form a tower of algebras. In this paper, we provide a diagrammatic approach to study the branching rules for cell modules on a tower of the partition algebras. This also allows us to calculate the structure constants of the Grothendieck ring of the tower.
Keywords
Cite
@article{arxiv.1908.03028,
title = {Branching rules for cell modules on a tower of the partition algebras},
author = {Pei Wang},
journal= {arXiv preprint arXiv:1908.03028},
year = {2025}
}
Comments
The main result of this paper has been proved by Bowman, De Visscher and Orellan (Trans. Amer. Math. Soc. (2015) 367, 3647--3667) . Therefore, I think this manuscript should be withdrawn