The Brauer algebra and a symplectic Schur functor

30 October 2008
Rudolf Tange
It is well-known that there is a strong link between the representation theories of the general linear group and the symmetric group over the complex numbers. J.A.Green has shown that this in also true over infinite fields of positive characteristic. For this he used the Schur functor as introduced by I.Schur in his PhD thesis. In this talk I will show that one can do the same thing for the symplectic group and the Brauer algebra. This is joint work with S.Donkin. As a consequence we obtain that (under certain conditions) the Brauer algebra and the symplectic Schur algebra in characteristic p have the same block relation. Furthermore we obtain a new proof of the description of the blocks of the Brauer algebra in characteristic zero as obtained by Cox, De Visscher and Martin.
  • Representation Theory Seminar