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The space of linear anti-symplectic involutions is a homogeneous space

Peter Albers, Urs Frauenfelder
published 2012-08-10

In this note we prove that the space of linear anti-symplectic involutions is the homogenous space $Gl(n,\R)\Sp(n)$. Furthermore, we show that the homogeneous space $U(n)/O(n)$, i.e. the Lagrangian Grassmannian, is diffeomorphic to $U(n)\cap\Sym(n)$.

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