Mirror symmetry, langlands duality, and the Hitchin system

T. Hausel, M. Thaddeus, Inventiones Mathematicae 153 (2003) 197–229.


Journal Article | Published
Author
;
Abstract
Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Stromdnger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equal. This provides significant evidence in support of SYZ. Moreover, the examples are of great interest in their own right: they are spaces of flat SLr-connections on a smooth curve. The mirror is the corresponding space for the Langlands dual group PGLr. These examples therefore throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.
Publishing Year
Date Published
2003-07-01
Journal Title
Inventiones Mathematicae
Volume
153
Issue
1
Page
197 - 229
IST-REx-ID

Cite this

Hausel T, Thaddeus M. Mirror symmetry, langlands duality, and the Hitchin system. Inventiones Mathematicae. 2003;153(1):197-229. doi:10.1007/s00222-003-0286-7
Hausel, T., & Thaddeus, M. (2003). Mirror symmetry, langlands duality, and the Hitchin system. Inventiones Mathematicae, 153(1), 197–229. https://doi.org/10.1007/s00222-003-0286-7
Hausel, Tamas, and Michael Thaddeus. “Mirror Symmetry, Langlands Duality, and the Hitchin System.” Inventiones Mathematicae 153, no. 1 (2003): 197–229. https://doi.org/10.1007/s00222-003-0286-7.
T. Hausel and M. Thaddeus, “Mirror symmetry, langlands duality, and the Hitchin system,” Inventiones Mathematicae, vol. 153, no. 1, pp. 197–229, 2003.
Hausel T, Thaddeus M. 2003. Mirror symmetry, langlands duality, and the Hitchin system. Inventiones Mathematicae. 153(1), 197–229.
Hausel, Tamas, and Michael Thaddeus. “Mirror Symmetry, Langlands Duality, and the Hitchin System.” Inventiones Mathematicae, vol. 153, no. 1, Springer, 2003, pp. 197–229, doi:10.1007/s00222-003-0286-7.

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