A characteristic free approach to Brauer algebras

Abstract

Abstract. Brauer algebras arise in representation theory of orthogonal or symplectic groups. These algebras are shown to be iterated inflations of group algebras of symmetric groups. In particular, they are cellular (as had been shown before by Graham and Lehrer). This gives some information about block decomposition of Brauer algebras.

The Birman–Murakami–Wenzl Algebras of Type Dn

“…This establishes that (Λ, T, C, * ) is a cell datum for A and so completes the proof of Theorem 1.2. Alternatively, the information we have provided shows B(D n ) is an iterated inflation of Hecke algebras of type D n , D n−2t , and A n−1−2s for s, t ≥ 1 and so are cellular by [19].…”

Brauer algebras of type C are cellularly stratified

“…The original definition of a cellular algebra, given by Graham and Lehrer in [5] has been shown to be equivalent to the following definition due to König and Xi [8].…”

The periplectic Brauer algebra

“…Theorems 1, 2 and 3 and other results in the paper lift the knowledge of the periplectic Brauer algebras, concerning quasi‐heredity, standardly based structures, block decomposition, Jucys–Murphy elements and Bartelli diagrams to the same level as that of the ordinary Brauer algebra. For , the corresponding topics were investigated in .…”