A lecture on invariant random subgroups

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Abstract

Invariant random subgroups (IRS) are conjugacy invariant probability measures on the space of subgroups in a given group G. They can be regarded both as a generalization of normal subgroups as well as a generalization of lattices. As such, it is intriguing to extend results from the theories of normal subgroups and of lattices to the context of IRS. Another approach is to analyse and then use the space IRS(G) as a compact G-space in order to establish new results about lattices. The second approach has been taken in the work [1], sometimes refered to as the seven samurai paper.1 In these lecture notes we shall try to give a taste of both approaches.

Original languageEnglish
Title of host publicationNew Directions in Locally Compact Groups
EditorsPierre-Emmanuel Caprace
PublisherCambridge University Press
Chapter13
Pages186-204
Number of pages19
ISBN (Electronic)9781108332675
ISBN (Print)9781108413121
DOIs
StatePublished - 8 May 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics

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