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arXiv · 2407.00961

The Hitchin Fibration for Symmetric Pairs

Thomas Hameister·Benedict Morrissey
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Abstract

We introduce and describe the "regular quotient" for the Hitchin fibration for symmetric spaces and explain some basic consequences for Higgs bundles. We include an invariant theoretic approach to spectral covers in this setting for the particular space $\mathrm{GL}_{2n}/(\mathrm{GL}_n\times \mathrm{GL}_n)$. We also include a study of the regular centralizer group scheme for quasisplit pairs, including a Galois description of a closely related group scheme. We collect some basic consequences for Hitchin systems associated to such pairs.

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Thomas Hameister, Benedict Morrissey. 2024-07-01. The Hitchin Fibration for Symmetric Pairs. https://arxiv.org/abs/2407.00961

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