Special Lagrangian linear subspaces in product symplectic space
Volume 65 / 2004
Banach Center Publications 65 (2004), 151-156
MSC: Primary 53D12, 51A50; Secondary 15A03, 53C38.
DOI: 10.4064/bc65-0-11
Abstract
The notes consist of a study of special Lagrangian linear subspaces. We will give a condition for the graph of a linear symplectomorphism $f:(\mathbb R^{2n},\sigma =\sum_{i=1}^n dx_i\wedge dy_i)\rightarrow (\mathbb R^{2n},\sigma)$ to be a special Lagrangian linear subspace in $(\mathbb R^{2n}\times \mathbb R^{2n},\omega=\pi^*_2\sigma -\pi^*_1\sigma)$. This way a special symplectic subset in the symplectic group is introduced. A stratification of special Lagrangian Grassmannian $S\Lambda_{2n}\simeq {SU(2n)/SO(2n)}$ is defined.
