Totally nonfree actions and infinite symmetric group

2011/09/15 by Vershik, Anatoly
#20B35 #22D40 #37A15 #Dynamical Systems (math.DS) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1109.3413

Abstract

We consider the totally nonfree (TNF) action of a groups and the corresponding adjoint invariant (AD) measures on the lattices of the subgroups of the given group. The main result is the description of all adjoint-invariant and TNF-measures on the lattice of subgroups of the infinite symmetric group S_{\Bbb N}. The problem is closely related to the theory of characters and factor representations of groups.

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