, Volume 34, Issue 1-2, pp 121-138

Amenable subgroups of semi-simple groups and proximal flows

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Abstract

We present a classification of maximal amenable subgroups of a semi-simple groupG. The result is that modulo a technical connectivity condition, there are precisely 2′ conjugacy classes of such subgroups ofG and we shall describe them explicitly. Herel is the split rank of the groupG. These groups are the isotropy groups of the action ofG on the Satake-Furstenberg compactification of the associated symmetric space and our results give necessary and sufficient conditions for a subgroup to have a fixed point in this compactification. We also study the action ofG on the set of all measures on its maximal boundary. One consequence of this is a proof that the algebraic hull of an amenable subgroup of a linear group is amenable.

Supported in part by NSF Grant No. MPS-74-19876.