Nets of Standard Subspaces on Non-compactly Causal Symmetric Spaces

Frahm J, Neeb KH, Òlafsson G (2025)

Publication Type: Book chapter / Article in edited volumes

Publication year: 2025

Publisher: Birkhauser

Series: Progress in Mathematics

Book Volume: 358

Pages Range: 115-195

DOI: 10.1007/978-981-97-7662-7_5

Abstract

Let G be a connected simple linear Lie group and H⊂G a symmetric subgroup such that the corresponding symmetric space G∕H is non-compactly causal. We show that any irreducible unitary representation of G leads naturally to a net of standard subspaces on G∕H that is isotone, covariant and has the Reeh–Schlieder and the Bisognano–Wichmann property. We also show that this result extends to the universal covering group of SL2(ℝ), which has some interesting application to intersections of standard subspaces associated to representations of such groups. For this, a detailed study of hyperfunction and distribution vectors is needed. In particular, we show that every H-finite hyperfunction vector is in fact a distribution vector.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Aarhus University DK Denmark (DK) Louisiana State University US United States (USA) (US)

How to cite

APA:

Frahm, J., Neeb, K.H., & Òlafsson, G. (2025). Nets of Standard Subspaces on Non-compactly Causal Symmetric Spaces. In (pp. 115-195). Birkhauser.

MLA:

Frahm, Jan, Karl Hermann Neeb, and Gestur Òlafsson. "Nets of Standard Subspaces on Non-compactly Causal Symmetric Spaces." Birkhauser, 2025. 115-195.

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