The Erdös-Ko-Rado theorem for vector spaces

Abstract Let V be an n-dimensional vector space over GF(q) and for integers k⩾t>0 let mq(n, k, t) denote the maximum possible number of subspaces in a t-intersecting family F of k-dimensional subspaces of V, i.e., dim F ∩ F′ ⩾ t holds for all F, F′ ϵ F . It is shown that m q (n,k,t)= max n−t k−t , 2k−t k for n⩾2k−t while for n⩽2k−t trivially m q (n,k,t)= n k holds.