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There are similarities between algebraic Lie theory and a geometricdescription of the blocks of the Brauer algebra in characteristic zero.Motivated by this, we study the alcove geometry of a certain reflection groupaction. We provide analogues of translation functors for a tower ofrecollement, and use these to construct Morita equivalences between blockscontaining weights in the same facet. Moreover, we show that the determinationof decomposition numbers for the Brauer algebra in characteristic zero can bereduced to a study of the block containing the weight 0. We define parabolicKazhdan-Lusztig polynomials for the Brauer algebra and show in certain low rankexamples that they determine standard module decomposition numbers andfiltrations.

Alcove geometry and a translation principle for the Brauer algebra