Title

SYMMETRIC SPACES WITH DISSECTING INVOLUTIONS

Document Type

Article

Publication Date

1-1-2020

Abstract

An involutive diffeomorphism σ of a connected smooth manifold M is called dissecting if the complement of its fixed point set is not connected. Dissecting involutions on a complete Riemannian manifold are closely related to constructive quantum field theory through the work of Dimock and Jaffe/Ritter on the construction of reflection positive Hilbert spaces. In this article we classify all pairs (M, σ), where M is an irreducible connected symmetric space, not necessarily Riemannian, and σ is a dissecting involutive automorphism. In particular, we show that the only irreducible, connected and simply connected Riemannian symmetric spaces with dissecting isometric involutions are Sn and ℍn, where the corresponding fixed point spaces are Sn−1 and ℍn − 1, respectively.

Publication Source (Journal or Book title)

Transformation Groups

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