The Semisimplicity of ω n f

Abstract

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A characteristic free approach to Brauer algebras

“…We have introduced this concept for general cellular algebras in [KX2] and shown (theorem 4.1 in [KX2]) that actually an algebra is cellular if and only if it is such an iterated inflation. Special cases of inflations can be found in the papers of Graham and Lehrer [GL], Hanlon and Wales [HW1] and even in the early studies of Brown [Brow1,Brow2,Brow3], who considered 'generalised matrix algebras' which coincide in his case with our inflations.…”

“…Of course, these filtrations have been used before, in particular in the semisimple case. Brown [Brow1,Brow2,Brow3] and Hanlon and Wales (see section 2 in [HW3]) used the subquotients in this filtration. The new point in our approach, however, is to identify these subquotients as inflations of group algebras of symmetric groups.…”

Brauer Algebras and Centralizer Algebras for SO(2n,C)

“…There were two papers in the 1950s w x by Brown 5,6 that discussed the Brauer algebras and partially determined when they are semisimple. However, it was not until the late 1980s that others began to look at these algebras with renewed interest because of their connections with other areas of mathematics.…”

Some Irreducible Representations of Brauer's Centralizer Algebras

“…THEOREM 1.1 ([1], [2], [3]). Let ϕ : B n (−2m) → End Sp(V ) (V ⊗n ) and ψ : ‫ރ‬Sp(V ) → End B n (−2m) (V ⊗n ) be the natural algebra homomorphisms.…”