Timeline for Why are Lagrangian subspaces in a symplectic vector space interesting?

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May 5, 2019 at 15:11	comment	added	Will Sawin		@AndySanders My answer was trying to focus on why we don't study the symplectic Grassmanian. No matter how interesting Lagrangian subspaces are, we would still study symplectic subspaces to if they were useful for something. I think their genericity largely explains why we do not.
May 5, 2019 at 15:02	comment	added	Andy Sanders		To a certain kind of person, I think this is the right, though certainly not only, answer. The basic structure theory of the symplectic group, in particular its parabolic subgroups, demands you give special privilege to isotropic, and therefore Lagrangian, sub-spaces. I wonder if this can somehow be turned into an explanation for the privileged role that Lagrangian sub-spaces, and sub-manifolds, play in symplectic geometry, complementing the physical reasons that they are so important.
Mar 23, 2019 at 0:44	history	answered	Will Sawin	CC BY-SA 4.0