Mirror symmetry, Langlands duality, and commuting elements of Lie groups

Details Mirror symmetry, Langlands duality, and commuting elements of Lie groups Mirror symmetry, Langlands duality, and commuting elements of Lie groups

2000-09-08

arxiv.org/abs/math/0009081v2

Mathematics

Algebraic Geometry

21 pages, LaTeX with packages amsfonts, amssym

Scientific paper

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).

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