On the Universal Embedding of the Sp2n(2) Dual Polar Space

A. E. Brouwer has shown that the universal embedding of the Sp2n(2) dual polar space has dimension at least (2n+1)(2n−1+1)/3 and has conjectured equality. The present paper settles this conjecture in the affirmative by proving a theorem about permutation modules for GLn(2) which implies the reverse inequality.