Invariant measures for algebraic actions, Zariski dense subgroups and Kazhdan’s property (t)

Yehuda Shalom*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let k be any locally compact non-discrete field. We show that finite invariant measures for k-algebraic actions are obtained only via actions of compact groups. This extends both Borel’s density and fixed point theorems over local fields (for semisimple/solvable groups, resp.). We then prove that for k-algebraic actions, finitely additive finite invariant measures are obtained only via actions of amenable groups. This gives a new criterion for Zariski density of subgroups and is shown to have representation theoretic applications. The main one is to Kazhdan’s property (T) for algebraic groups, which we investigate and strengthen.

Original languageEnglish
Pages (from-to)3387-3412
Number of pages26
JournalTransactions of the American Mathematical Society
Volume351
Issue number8
DOIs
StatePublished - 1999
Externally publishedYes

Fingerprint

Dive into the research topics of 'Invariant measures for algebraic actions, Zariski dense subgroups and Kazhdan’s property (t)'. Together they form a unique fingerprint.

Cite this