Young modules and filtration multiplicities for Brauer algebras.
This paper aims to generalize the Young modules theory for symmetric groups to the Brauer algebra \(B_k(r,\delta)\). The authors define permutation modules and Young modules for \(B_k(r,\delta)\), and show that if the characteristic of the field \(k\) is neither \(2\) nor \(3\) then every permutation module is a sum of Young modules. Moreover, the authors determine precisely in which cases cell module filtration multiplicities are well-defined, which generalizes earlier results of Hemmer-Nakano for symmetric groups.
scientific article; zbMATH DE number 5076564