Koszul gradings on Brauer algebras

We show that the Brauer algebra Brd(δ) over the complex numbers for an integral parameter δ can be equipped with a grading. In case δ ≠ 0, it becomes a graded quasihereditary algebra which is moreover Morita equivalent to a Koszul algebra. These results are obtained by realizing the Brauer algebra as an idempotent truncation of a certain level two VW-algebra W^cycl_d (N) for some large positive integral parameter N. The parameter δ appears here in the choice of a cyclotomic quotient. This cyclotomic VW-algebra arises naturally as an endomorphism algebra of a certain projective module in parabolic category O of type D. In particular, the graded decomposition numbers are given by the associated parabolic Kazhdan-Lusztig polynomials.