Linear phase space deformations with angular momentum symmetry

Claudio Meneses

doi:10.3934/jgm.2019003

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2019, Volume 11, Issue 1: 45-58. Doi: 10.3934/jgm.2019003

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Linear phase space deformations with angular momentum symmetry

Claudio Meneses^,

Mathematisches Seminar, Christian-Albrechts Universität zu Kiel, Ludewig-Meyn-Str. 4, 24118 Kiel, Germany

* Corresponding author: Claudio Meneses
* Corresponding author: Claudio Meneses

Received: March 2018

Revised: November 2018

Published online: March 2019

The author is supported by the DFG SPP 2026 priority programme "Geometry at infinity".

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Abstract

Motivated by the work of Leznov-Mostovoy [17], 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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Mathematics Subject Classification: Primary: 17B08, 17B56, 17B80; Secondary: 53D20, 14H70.

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