Linear phase space deformations with angular momentum symmetry

Abstract

Motivated by the work of Leznov--Mostovoy, we classify the linear deformations of standard $2n$-dimensional phase space that preserve the obvious symplectic $\mathfrak{o}(n)$-symmetry. As a consequence, we describe standard phase space, as well as $T^{\ast }{S}^n$ and $T^{\ast }{\mathbb{H}}^n$ with their standard symplectic forms, as degenerations of a 3-dimensional family of coadjoint orbits, which in a generic regime are identified with the Grassmannian of oriented 2-planes in ${\mathbb{R}}^{n+2}$.

16 pages. Final version