  There are similarities between algebraic Lie theory and a geometric
description of the blocks of the Brauer algebra in characteristic zero.
Motivated by this, we study the alcove geometry of a certain reflection group
action. We provide analogues of translation functors for a tower of
recollement, and use these to construct Morita equivalences between blocks
containing weights in the same facet. Moreover, we show that the determination
of decomposition numbers for the Brauer algebra in characteristic zero can be
reduced to a study of the block containing the weight 0. We define parabolic
Kazhdan-Lusztig polynomials for the Brauer algebra and show in certain low rank
examples that they determine standard module decomposition numbers and
filtrations.
