Infinite p-adic random matrices and ergodic decomposition of p-adic Hua measures

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Abstract

Neretin constructed an analogue of the Hua measures on the infinite p-adic matrices Mat(N,Qp). Bufetov and Qiu classified the ergodic measures on Mat(N,Qp) that are invariant under the natural action of GL(∞,Zp)×GL(∞,Zp). In this paper we solve the problem of ergodic decomposition for the p-adic Hua measures introduced by Neretin. We prove that the probability measure governing the ergodic decomposition has an explicit expression which identifies it with a Hall-Littlewood measure on partitions. Our arguments involve certain Markov chains.
Original languageEnglish
Number of pages27
JournalTransactions of the American Mathematical Society
Publication statusAccepted/In press - 27 Jul 2021

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