# Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve

Hausel T. 2005.Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve. In: Geometric Methods in Algebra and Number Theory. Progress in Mathematics, vol. 235, 193–217.

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Progress in Mathematics

Abstract

The paper surveys the mirror symmetry conjectures of Hausel-Thaddeus and Hausel-Rodriguez-Villegas concerning the equality of certain Hodge numbers of SL(n, ℂ) vs. PGL(n, ℂ) flat connections and character varieties for curves, respectively. Several new results and conjectures and their relations to works of Hitchin, Gothen, Garsia-Haiman and Earl-Kirwan are explained. These use the representation theory of finite groups of Lie-type via the arithmetic of character varieties and lead to an unexpected conjecture for a Hard Lefschetz theorem for their cohomology.

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2005-01-01

Book Title

Geometric Methods in Algebra and Number Theory

Volume

235

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193 - 217

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### Cite this

Hausel T. Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve. In:

*Geometric Methods in Algebra and Number Theory*. Vol 235. Springer; 2005:193-217. doi:10.1007/0-8176-4417-2_9Hausel, T. (2005). Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve. In

*Geometric Methods in Algebra and Number Theory*(Vol. 235, pp. 193–217). Springer. https://doi.org/10.1007/0-8176-4417-2_9Hausel, Tamás. “Mirror Symmetry and Langlands Duality in the Non-Abelian Hodge Theory of a Curve.” In

*Geometric Methods in Algebra and Number Theory*, 235:193–217. Springer, 2005. https://doi.org/10.1007/0-8176-4417-2_9.T. Hausel, “Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve,” in

*Geometric Methods in Algebra and Number Theory*, vol. 235, Springer, 2005, pp. 193–217.Hausel, Tamás. “Mirror Symmetry and Langlands Duality in the Non-Abelian Hodge Theory of a Curve.”

*Geometric Methods in Algebra and Number Theory*, vol. 235, Springer, 2005, pp. 193–217, doi:10.1007/0-8176-4417-2_9.**All files available under the following license(s):**

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