O(∞)- and Sp(∞)-Invariant Ergodic Measures on the Spaces of Infinite Antisymmetric and Quaternionic Antihermitian Matrices

Аннотация

The ergodic measures for the actions of the infinite orthogonal group O(∞) and the infinite symplectic group Sp(∞) 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.”