$O(\infty)$- and $\mathrm{Sp}(\infty)$-invariant ergodic measures on the spaces of infinite antisymmetric and quaternionic antihermitian matrices

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.”