Abstract:

The Brauer algebras of type C arise as subalgebras of the classical Brauer algebras, spanned by all symmetric diagrams. In this talk, we will explore the construction of permutation modules and Young modules for Brauer algebras of type C by extending the representation theory of the group algebra of hyperoctahedral groups. We further establish a stratifying system for the Brauer algebras of type C, generalizing the work of Hemmer and Nakano on Hecke algebras. This framework allows us to determine when the multiplicities of cell modules in any filtration are well-defined. As a consequence, we show that if the characteristic of the field is neither 2 nor 3, then every permutation module for the Brauer algebra of type C decomposes as a direct sum of indecomposable Young modules. (This is joint work with Geetha Thangavelu.)