PUB - Publikationen an der Universität Bielefeld

Let V be a linear space over a field K of dimension n > 1, and let be an irreducible linear group. In this paper we prove that the group G contains an element g such that rank for every , where E (n) is the identity operator on V. This estimate is sharp for any . The existence of such an element implies that the conjugacy class of G in GL(V) intersects the big Bruhat cell of GL(V) non-trivially (here B is a fixed Borel subgroup of G). The latter fact is equivalent to the existence of a complete flag such that the flags are in general position for some g a G.