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A Banachic generalization of Shalom's property H_FD.

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NPC - Non-positive curvature group actions and cohomology

A group has property H_FD if the first reduced cohomology of unitary representations is supported on finite sub-representations. Shalom has proved that this property is stable under quasi-isometry among amenable groups. We generalize this notion to the class of WAP representations, and we prove that this stronger property holds for a class of locally compact solvable groups including algebraic groups over local fields and their lattices. As a by-product we prove a conjecture of Shalom, namely that solvable finitely generated subgroups of GL(Q) have H_FD.   (Joint work with Yves Cornulier)



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