Ergodic measures on infinite skew-symmetric matrices over non-Archimedean local fields · arXivDesk1606.00293Jun 1, 2016Skew-symmetric case of similar results in a previous paper, with simplified presentation. 12 pages
Ergodic measures on infinite skew-symmetric matrices over non-Archimedean local fields
Yanqi Qiu
Abstract
Let F be a non-discrete non-Archimedean locally compact field such that the characteristic ch(F)=2 and let OF
be the ring of integers in
. The main results of this paper are Theorem 1.2 that classifies ergodic probability measures on the space
Skew(N,F) of infinite skew-symmetric matrices with respect to the natural action of the group
GL(∞,OF) and Theorem 1.4, that gives an unexpected natural correspondence between the set of
GL(∞,OF) -invariant Borel probability measures on
Sym(N,F) with the set of
GL(∞,OF)×GL(∞,OF) -invariant Borel probability measures on the space
Mat(N,F) of infinite matrices over
.