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A Banachic generalization of Shalom's property H_FD.

Presented by: 
Romain Tessera
Thursday 2nd March 2017 - 10:00 to 12:00
INI Seminar Room 2
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons