For 1 ≤ p ≤ 2, Gr_res,p(H) is an affine coadjoint orbit of U_res,p(H) admitting weak symplectic structures induced by a non-trivial 2-cocycle on the Lie algebra.
H.,Infinite-Dimensional Groups and Their Representations, Lie Theory: Lie Algebras and Representations, 213–328, Birkh¨ auser Boston 2004
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The Restricted Schatten-class Grassmannian $\mathrm{Gr}_{\mathrm{res}, p}(\mathcal{H})$ as affine coadjoint orbit
For 1 ≤ p ≤ 2, Gr_res,p(H) is an affine coadjoint orbit of U_res,p(H) admitting weak symplectic structures induced by a non-trivial 2-cocycle on the Lie algebra.