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

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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).
21 pages, LaTeX with packages amsfonts, amssym

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Algebraic Geometry, High Energy Physics - Theory, Mathematical Physics, Symplectic Geometry, 14J32 (Primary); 14H60, 14J60, 20G20, 37J35 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/59893

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0009081
 http://arxiv.org/abs/math/0009081

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arXiv