Mirror symmetry, Langlands duality, and commuting elements of Lie groups
Algebraic Geometry
2007-05-23 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Symplectic Geometry
Abstract
By normalizing the space of commuting pairs of elements in a reductive Lie group G, and the corresponding space for the Langlands dual group, we construct pairs of hyperkahler orbifolds which satisfy the conditions to be mirror partners in the sense of Strominger-Yau-Zaslow. The same holds true for commuting quadruples in a compact Lie group. The Hodge numbers of the mirror partners, or more precisely their orbifold E-polynomials, are shown to agree, as predicted by mirror symmetry. These polynomials are explicitly calculated when G is a quotient of SL(n).
Keywords
Cite
@article{arxiv.math/0009081,
title = {Mirror symmetry, Langlands duality, and commuting elements of Lie groups},
author = {Michael Thaddeus},
journal= {arXiv preprint arXiv:math/0009081},
year = {2007}
}
Comments
21 pages, LaTeX with packages amsfonts, amssym