On the universal embedding of the Sp(2n)(2) dual polar space

摘要

A. E. Brouwer has shown that the universal embedding of the Sp(2n)(2) dual polar space has dimension at least ( 2(n) + 1)(2(n-1) + 1)/3 and has conjectured equality. The present paper settles this conjecture in thr affirmative by proving a theorem about permutation modules for GL(n)(2) which implies tile reverse inequality. (C) 2001 Academic Press. [References: 6]