
TL;DR
This paper extends Tannaka-Krein duality to metric groups, establishing a dual metric on representations and exploring conditions for metric recovery and applications to T-duality and quantum Gromov-Hausdorff distance.
Contribution
It introduces a framework for incorporating metrics into Tannaka-Krein duality, defining dual metrics on representation categories and analyzing metric recovery conditions.
Findings
Defined dual metrics on representation categories for metric groups.
Characterized conditions for recovering the original metric from the dual.
Explored applications to T-duality and quantum Gromov-Hausdorff distance.
Abstract
We incorporate metric data into the framework of Tannaka-Krein duality. Thus, for any group with left invariant metric, we produce a dual metric on its category of unitary representations. We characterize the conditions under which a "double-dual" metric on the group may be recovered from the metric on representations, and provide conditions under which a metric agrees with its double-dual. We also consider some applications to T-duality and quantum Gromov-Hausdorff distance.
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.
