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 \( {\mathbbm{S}}^n \) and ℍn, where the corresponding fixed point spaces are \( {\mathbbm{S}}^{n-1} \) and ℍn − 1, respectively.
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K.-H. Neeb is supported by DFG-grant NE 413/9-1.
G. Ólafsson is supported by Simons grant 586106.
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NEEB, KH., ÓLAFSSON, G. SYMMETRIC SPACES WITH DISSECTING INVOLUTIONS. Transformation Groups 27, 635–649 (2022). https://doi.org/10.1007/s00031-020-09595-z
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DOI: https://doi.org/10.1007/s00031-020-09595-z