Enhanced mirror symmetry for Langlands dual Hitchin systems
Tam\'as Hausel
TL;DR
This paper surveys mirror symmetry between Langlands dual Hitchin systems and introduces conjectural structures on their mirrors, focusing on multiplicity algebras and Lagrangian subvarieties.
Contribution
It provides a comprehensive survey of existing results and proposes new conjectural frameworks for mirror symmetry in Hitchin systems.
Findings
Summary of mathematical results on mirror symmetry for Hitchin systems
Introduction of multiplicity algebras on Lagrangians in Hitchin systems
Discussion of conjectural structures on the mirror side
Abstract
The first part of this paper is a survey of mathematical results on mirror symmetry phenomena between Hitchin systems for Langlands dual groups. The second part introduces and discusses multiplicity algebras of the Hitchin system on Lagrangians, and considers corresponding conjectural structures on their mirror.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models