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arXiv · 1403.0698

Satake diagrams and real structures on spherical varieties

Dmitri Akhiezer
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Abstract

With each antiholomorphic involution $σ$ of a connected complex semisimple Lie group $G$ we associate an automorphism $ε_σ$ of the Dynkin diagram. The definition of $ε_σ$ is given in terms of the Satake diagram of $σ$. Let $H \subset G$ be a self-normalizing spherical subgroup. If $ε_σ={\rm id}$ then we prove the uniqueness and existence of a $σ$-equivariant real structure on $G/H$ and on the wonderful completion of $G/H$.

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Dmitri Akhiezer. 2015-10-05. Satake diagrams and real structures on spherical varieties. https://doi.org/10.1142/s0129167x15501037

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