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The notes consist of a study of special Lagrangian linear subspaces. We will give a condition for the graph of a linear symplectomorphism $f:({ℝ}^{2n},\sigma ={\sum }_{i=1}^{n}d{x}_i\wedge d{y}_i)\to ({ℝ}^{2n},\sigma )$ to be a special Lagrangian linear subspace in $({ℝ}^{2n}\times {ℝ}^{2n},\omega =\pi *₂\sigma -\pi *₁\sigma )$. This way a special symplectic subset in the symplectic group is introduced. A stratification of special Lagrangian Grassmannian $S{\Lambda }_{2n}\simeq SU\left(2n\right)/SO\left(2n\right)$ is defined.

We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of the Thom polynomials of Lagrange singularities always have nonnegative coefficients. This is an analog of a result on the Thom polynomials of mapping singularities and Schur S-functions, established formerly by the last two authors.