(1, 2)-Symplectic Metrics, Flag Manifolds and Tournaments

It has recently been shown by Mo and Negreiros that a necessarycondition for an invariant almost complex structure on the complexfull flag manifold F(n) to admit a (1, 2)-symplectic invariantmetric is that its associated tournament be cone-free. In thispaper, a canonical stair-shaped form is given for such tournaments,and this is applied to show that the condition is also sufficient;in the process, all the associated (1, 2)-symplectic metricsare described. 2000 Mathematics Subject Classification 53C55,05C20, 58E20.