Property (T_B) and Property (F_B) restricted to an irreducible representation

Details Property (T_B) and Property (F_B) restricted to an irreducible representation Property (T_B) and Property (F_B) restricted to an irreducible representation

2011-04-07

arxiv.org/abs/1104.1261v2

Mathematics

Group Theory

17 pages

Scientific paper

In this paper, we give a necessary and sufficient condition for which a finitely generated group has a property like Kazhdan's Property (T) restricted to one irreducible isometric representation on a strictly convex Banach space. Similary, we give a necessary and sufficient condition for which a finitely generated group has a property like Property (FH) restricted to the set of the affine isometric actions whose linear part are one irreducible isometric representation on a strictly convex Banach space. If the Banach space is the l^p space (1

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