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(1, 2)‐Symplectic Metrics, Flag Manifolds and Tournaments
Author(s) -
Cohen Nir,
Negreiros Caio J. C.,
San Martin Luiz A. B.
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930200142x
Subject(s) - mathematics , symplectic geometry , flag (linear algebra) , invariant (physics) , pure mathematics , symplectic manifold , tournament , combinatorics , algebra over a field , mathematical physics
It has recently been shown by Mo and Negreiros that a necessary condition for an invariant almost complex structure on the complex full flag manifold F( n ) to admit a (1, 2)‐symplectic invariant metric is that its associated tournament be cone‐free. In this paper, 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 metrics are described. 2000 Mathematics Subject Classification 53C55, 05C20, 58E20.