Representing groups against all odds

We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups admit nonabelian free subgroups in that measure-theoretical sense. Consequences for affine actions and for unitarizability are then drawn. In particular, we obtain a new characterization of amenability via some affine actions on Hilbert spaces. Along the way, various fixed-point properties for groups are studied. We also give a survey of several useful facts about group representations on Banach spaces, continuity of group actions, compactness of convex hulls in locally convex spaces, and measurability pathologies in Banach spaces.


Advisor(s):
Monod, Nicolas
Year:
2017
Publisher:
Lausanne, EPFL
Keywords:
Other identifiers:
urn: urn:nbn:ch:bel-epfl-thesis7823-1
Laboratories:




 Record created 2017-08-21, last modified 2018-01-28

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