A geometric characterisation of the blocks of the Brauer algebra

Abstract

We give a geometric description of the blocks of the Brauer algebra $B_n(\delta )$ in characteristic zero as orbits of the Weyl group of type $D_n$. We show how the corresponding affine Weyl group controls the representation theory of the Brauer algebra in positive characteristic, with orbits corresponding to unions of blocks.

26 pages, 24 figures

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