Timeline for measuring $n\ 2$-planes in $\mathbb{R}^{2n}$
Current License: CC BY-SA 3.0
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| Mar 13, 2012 at 3:35 | comment | added | JHM | Well, here's a special situation: say we have a lattice L and an integral unimodular symplectic form \omega defined on L. Moreover say we have a symplectic basis e_1, .., e_n, f_1, .., f_n \in L. Then each pair e_i, f_i span a rational symplectic subspace P_i of the lattice. As measure on P_i we can take the eccentricity k_i of the convex hull of {e_i, f_i} (an ellipse). This describes an n-fold continuous measure {k_1, ..., k_n} on the symplectic bases (e_1, ..., f_n). But again, this a special special little situation. | |
| Mar 13, 2012 at 0:49 | history | answered | Victor Dods | CC BY-SA 3.0 |