Branching rules for cell modules on a tower of the partition algebras
arXiv:1908.03028
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.
arXiv commentThe 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 Therefore, I think this manuscript should be withdrawn