Let be a finite-dimensional real vector space and a compact simple Lie group with Lie algebra . Consider the Fréchet–Lie group of -jets at of smooth maps , with Lie algebra . Let be a Lie group and write . Let be a smooth -action on . We study smooth projective unitary representations of that satisfy a so-called generalized positive energy condition. In particular, this class captures representations that are in a suitable sense compatible with a KMS state on the von Neumann algebra generated by . We show that this condition imposes severe restrictions on the derived representation of , leading in particular to sufficient conditions for to factor through , or even through .
Cite this article
Milan Niestijl, Generalized positive energy representations of groups of jets. Doc. Math. 28 (2023), no. 3, pp. 709–763DOI 10.4171/DM/920