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arXiv · 1803.08895

Linear phase space deformations with angular momentum symmetry

Claudio Meneses
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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 $T^{*}S^{n}$ and $T^{*}\mathbb{H}^{n}$ 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 $\mathbb{R}^{n+2}$.

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Claudio Meneses. 2018-03-23. Linear phase space deformations with angular momentum symmetry. https://doi.org/10.3934/jgm.2019003

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