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Special Lagrangian linear subspaces in product symplectic space

Małgorzata Mikosz (2004)

Banach Center Publications

The notes consist of a study of special Lagrangian linear subspaces. We will give a condition for the graph of a linear symplectomorphism f : ( 2 n , σ = i = 1 n d x i d y i ) ( 2 n , σ ) to be a special Lagrangian linear subspace in ( 2 n × 2 n , ω = π * σ - π * σ ) . This way a special symplectic subset in the symplectic group is introduced. A stratification of special Lagrangian Grassmannian S Λ 2 n S U ( 2 n ) / S O ( 2 n ) is defined.

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