TY - CHAP
AB - 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.
AU - Tamas Hausel
ID - 1444
T2 - Geometric Methods in Algebra and Number Theory
TI - Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve
VL - 235
ER -