Cayley correspondences and dual Hitchin fibers
Organizers
Speaker
Time
Thursday, October 8, 2026 3:00 PM - 4:00 PM
Venue
A7-201
Online
Zoom 638 227 8222
(BIMSA)
Abstract
The classical Cayley correspondence parametrizes certain connected components of moduli spaces of real-group Higgs bundles by twisted Higgs bundles and holomorphic differentials. We extend this construction to a morphism of moduli stacks. Using the global moment-map construction, we equip the map from the Cayley stack to the moduli stack of complex-group Higgs bundles with a derived Lagrangian structure.
We then study these Cayley Lagrangians through relative Langlands duality, which predicts a duality between Hamiltonian spaces for Langlands dual groups. For three strictly quasi-split families, over a suitable open subset of the Hitchin base, we identify the coarse neutral Cayley fiber with the dual of the quotient of the ambient Langlands-dual Hitchin fiber by the spherical dual subgroup’s Hitchin fiber. The key geometric observation is that the quotient and the Cayley fiber arise from the same smaller, twisted type A Hitchin system. This yields a fiberwise Dolbeault verification of the predicted dual support.
This is joint work with Eric Yen-Yo Chen and Enya Hsiao.
We then study these Cayley Lagrangians through relative Langlands duality, which predicts a duality between Hamiltonian spaces for Langlands dual groups. For three strictly quasi-split families, over a suitable open subset of the Hitchin base, we identify the coarse neutral Cayley fiber with the dual of the quotient of the ambient Langlands-dual Hitchin fiber by the spherical dual subgroup’s Hitchin fiber. The key geometric observation is that the quotient and the Cayley fiber arise from the same smaller, twisted type A Hitchin system. This yields a fiberwise Dolbeault verification of the predicted dual support.
This is joint work with Eric Yen-Yo Chen and Enya Hsiao.