Noncommutative Geometry Seminar

Date: June 17, 2020

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Shintaro Nishikawa, Penn State University

Title: Sp(n,1) admits a proper 1-cocycle for a uniformly bounded representation

Abstract: We show that the simple rank one Lie group Sp(n ,1) for any n admits a proper 1-cocycle for a uniformly bounded Hilbert space representation: i.e. it admits a metrically proper affine action on a Hilbert space whose linear part is a uniformly bounded representation. Our construction is a simple modification of the one given by Pierre Julg but crucially uses results on uniformly bounded representations by Michael Cowling. An interesting new feature is that the properness of these cocycles follows from the non-continuity of a critical case of the Sobolev embedding. This work is inspired from Pierre Julg's work on the Baum-Connes conjecture for Sp(n,1).

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