Title: On strong property (T) and fixed point properties for Lie groups
Authors: de Laat, Tim * #
Mimura, Masato * #
de la Salle, Mikael * # ×
Issue Date: 2016
Publisher: Impr. Durand
Series Title: Annales de l'Institut Fourier vol:66 issue:5 pages:1859-1893
Abstract: We consider certain strengthenings of property (T) relative to Banach spaces that are satisfied by high rank Lie groups. Let X be a Banach space for which, for all k, the Banach-Mazur distance to a Hilbert space of all k-dimensional subspaces is bounded above by a power of k strictly less than one half. We prove that every connected simple Lie group of sufficiently large real rank depending on X has strong property (T) of Lafforgue with respect to X. As a consequence, we obtain that every continuous affine isometric action of such a high rank group (or a lattice in such a group) on X has a fixed point. This result corroborates a conjecture of Bader, Furman, Gelander and Monod. For the special linear Lie groups, we also present a more direct approach to fixed point properties, or, more precisely, to the boundedness of quasi-cocycles. Without appealing to strong property (T), we prove that given a Banach space X as above, every special linear group of sufficiently large rank satisfies the following property: every quasi-1-cocycle with values in an isometric representation on X is bounded.
ISSN: 0373-0956
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
* (joint) first author
× corresponding author
# (joint) last author

Files in This Item:
File Description Status SizeFormat
dLMdlS - AIF.pdf Published 760KbAdobe PDFView/Open


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science