标题： Young模的构造及类型$C$的Brauer代数的滤链乘数 显示英文标题

标题： Construction of Young modules and filtration multiplicities for Brauer algebras of type $C$

摘要： 在本文中，我们通过扩展超八面体群的群代数表示理论，构建了类型$C$的Brauer代数的置换模和Young模。 此外，我们为类型$C$的Brauer代数开发了一个分层系统，从而扩展了Hemmer-Nakano在\cite{HN}中对Hecke代数的工作。 这个框架使我们能够确定在任何滤链中细胞模的重数是否定义良好。 作为结果，我们证明了如果域的特征既不是$2$也不是$3$，那么类型$C$的Brauer代数的每个置换模都可以分解为不可约Young模的直和。 我们还建立了超八面体群的群代数的一些上同调条件，这些条件是证明类型$C$的Brauer代数结果所必需的。 显示英文摘要

摘要： In this paper, we construct the permutation modules and Young modules for Brauer algebras of type $C$ by extending the representation theory of the group algebra of hyperoctahedral groups. Additionally, we develop a stratifying system for Brauer algebras of type $C$, thereby extending the work of Hemmer-Nakano in \cite{HN} on Hecke algebras. This framework allows us to determine when the multiplicities of cell modules in any filtration are well-defined. As a result, we prove that if the characteristic of the field is neither $2$ nor $3$, then every permutation module of the Brauer algebra of type $C$ decomposes into a direct sum of indecomposable Young modules. We also establish certain cohomological criteria for the group algebra of the hyperoctahedral groups, which are necessary to prove the results for the Brauer algebras of type $C$.