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

T. Hausel, in:, Geometric Methods in Algebra and Number Theory, Springer, 2005, pp. 193–217.


Book Chapter | Published
Series Title
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.
Publishing Year
Date Published
2005-01-01
Book Title
Geometric Methods in Algebra and Number Theory
Volume
235
Page
193 - 217
IST-REx-ID

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