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In this paper we present two dual pairs that can be seen as the linear analogues of the following two dual pairs related to fluids: the EPDiff dual pair due to Holm and Marsden, and the ideal fluid dual pair due to Marsden and Weinstein. [ABSTRACT FROM AUTHOR]

Motivated by the work of Leznov-Mostovoy [17], we classify the linear deformations of standard 2n-dimensional phase space that preserve the obvious symplectic o(n)-symmetry. As a consequence, we describe standard phase space, as well as T∗Sn and T∗Hn 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 Rn+2. [ABSTRACT FROM AUTHOR]