  The longstanding Alperin weight conjecture and its blockwise version have
been reduced to simple groups recently by Navarro, Tiep, Spaeth and Koshitani.
Thus, to prove this conjecture, it suffices to verify the corresponding
inductive condition for all finite simple groups. The first is to establish an
equivariant bijection between irreducible Brauer characters and weights for the
universal covering groups of simple groups. Assume q is a power of some odd
prime p. We first prove the blockwise Alperin weight conjecture for Sp2n(q) and
odd non-defining characteristics. If the decomposition matrix of Sp2n(q) is
unitriangular with respect to an Aut(Sp2n(q))-stable basic set (this assumption
holds for linear primes), we can establish an equivariant bijection between the
irreducible Brauer characters and weights.
