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arXiv · 2509.16166

Symmetric Spaces with Rectangular Unit Lattices, Revisited

Jost-Hinrich Eschenburg·Ernst Heintze·Peter Quast
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Abstract

We give a new proof of a theorem of Loos stating that a Riemannian symmetric space X with rectangular unit lattice is a symmetric R-space. For this we construct explicitly an isometric extrinsically symmetric embedding of X in a Euclidean space which reveals X as a standardly embedded symmetric R-space. We further determine the root systems, Euclidean root data, fundamental groups and eigenvalues of the Laplacian of symmetric spaces with rectangular unit lattice in a direct way.

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Jost-Hinrich Eschenburg, Ernst Heintze, Peter Quast. 2025-09-19. Symmetric Spaces with Rectangular Unit Lattices, Revisited. https://arxiv.org/abs/2509.16166

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