Nets of Standard Subspaces on Non-compactly Causal Symmetric Spaces

Document Type

Article

Publication Date

1-1-2025

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.

Publication Source (Journal or Book title)

Progress in Mathematics

First Page

115

Last Page

195

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