Li, Ping et Su, Yang, The signature of generalized flag manifolds and applications, Acta mathematica Sinica. English series (Print) , 26(8), 2010, pp. 1457-1462
Let G be a linear algebraic group over . and P be a parabolic subgroup. We determine the signatures of the flag manifold G/P. As an application, we prove that the nonsingular hypersurfaces of degree 2 in .P n are prime if n satisfies certain conditions.