On the Universal Embedding of the U2n(2) Dual Polar Space

A. E. Brouwer has shown that the universal embedding of the U2n(2) dual polar space has dimension at least (4n+2)/3 and has conjectured equality. The present paper proves this conjecture by establishing a related result about permutation modules for GLn(4). The method is the same used in the authorʹs previous paper on an analogous question for the Sp2n(2) dual polar space.