Geodesic
$O(\infty)$- and $\mathrm{Sp}(\infty)$-invariant ergodic measures on the spaces of infinite antisymmetric and quaternionic antihermitian matrices
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXVI. Representation theory, dynamical systems, combinatorial methods, Tome 437 (2015), pp. 207-220 
P. P. Nikitin. $O(\infty)$- and $\mathrm{Sp}(\infty)$-invariant ergodic measures on the spaces of infinite antisymmetric and quaternionic antihermitian matrices. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXVI. Representation theory, dynamical systems, combinatorial methods, Tome 437 (2015), pp. 207-220. http://geodesic.mathdoc.fr/item/ZNSL_2015_437_a9/
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     title = {$O(\infty)$- and $\mathrm{Sp}(\infty)$-invariant ergodic measures on the spaces of infinite antisymmetric and quaternionic antihermitian matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {207--220},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_437_a9/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The ergodic measures for the actions of the infinite orthogonal group $O(\infty)$ and the infinite symplectic group $\mathrm{Sp}(\infty)$ by conjugations on the spaces of infinite real antisymmetric and infinite quaternionic antihermitian matrices are classified, with the use of the Vershik–Olshanski “ergodic method.”

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