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arXiv · 2312.05711

Spectral Data of Special Orthogonal Higgs Bundles and Hecke Modification

Tyson Klingner
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Abstract

We give a complete, self-contained computation of the spectral data parametrising Higgs bundles in the generic fibres of the $\mathrm{SO}_{2n+1}$-Hitchin fibration where the Higgs fields are $L$-twisted endomorphisms. Although the spectral data is known in the literature, we develop a new approach to spectral data, which takes advantage of Hecke modification. Further, we present the computation for the $\mathrm{Sp}_{2n}$ and $\mathrm{SO}_{2n}$ cases while clarifying some aspects of the correspondence which are not well explained in the pre-existing literature. We also compute the number of connected components of the generic fibres, and demonstrate Langlands duality in the fibres via the canonical duality in the fibres.

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Tyson Klingner. 2023-12-09. Spectral Data of Special Orthogonal Higgs Bundles and Hecke Modification. https://arxiv.org/abs/2312.05711

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