Property RD and hypercontractivity for orthogonal free quantum groups
Michael Brannan, Roland Vergnioux, Sang-Gyun Youn
TL;DR
This paper investigates property rapid decay (RD) and hypercontractivity in orthogonal free quantum groups, establishing failure of twisted RD in non Kac cases and improving hypercontractivity estimates in the Kac case.
Contribution
It demonstrates the failure of twisted property RD in non Kac orthogonal free quantum groups and provides new hypercontractivity bounds for heat semigroups.
Findings
Twisted property RD fails in non Kac cases.
New non-commutative Khintchine inequality for free groups.
Improved hypercontractivity estimates for quantum groups.
Abstract
We prove that the twisted property RD fails to hold for all non Kac type, non amenable orthogonal free quantum groups. In the Kac case we revisit property RD, proving an analogue of the non-commutative Khintchine inequality for free groups. As an application, we give new and improved hypercontractivity and ultracontractivity estimates for the generalized heat semigroups on free orthogonal quantum groups, both in the Kac and non Kac cases.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.