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arXiv · 2608.15186

A Unified Construction of Exceptional Symmetric Spaces

Yuuki Sasaki
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Abstract

We present a unified construction of all simply connected irreducible exceptional compact symmetric spaces as totally geodesic submanifolds of $E_{8}$. Using this construction, we obtain a unified description of totally geodesic embeddings between exceptional symmetric spaces by determining all inclusion relations among them. The resulting inclusion structure exhibits a remarkable and unexpected symmetry, suggesting a deeper geometric relationship among exceptional symmetric spaces.

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Yuuki Sasaki. 2026-08-15. A Unified Construction of Exceptional Symmetric Spaces. https://arxiv.org/abs/2608.15186

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