Ergodic measures on infinite skew-symmetric matrices over non-Archimedean local fields

2016/06/01 by Yanqi Qiu, Qiu, Yanqi
Mathematics · #Advanced Algebra and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1606.00293

openalex publication_date 2016/06/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

Let F be a non-discrete non-Archimedean locally compact field such that the characteristic ch(F)≠ 2 and let O_F be the ring of integers in F. 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(∞,O_F) and Theorem 1.4, that gives an unexpected natural correspondence between the set of GL(∞,O_F)-invariant Borel probability measures on Sym(ℕ, F) with the set of GL(∞,O_F) × GL(∞,O_F)-invariant Borel probability measures on the space Mat(ℕ, F) of infinite matrices over F.

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