Edward Witten Mirror Symmetry, Hitchin's Equations, And Langlands Duality "2. Mirror Symmetry And Hitchin’s Equations" "3. The Hitchin Fibration" "3.1. A Few Hints."・・・か これがどれだけNgo は Fundamental Lemmaに寄与したか不明だが Langlands DualityもMirror Symmetryに呑み込まれようとしている・・
arxiv.org/abs/0802.0999 Mirror Symmetry, Hitchin's Equations, And Langlands Duality Edward Witten (Submitted on 7 Feb 2008) Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold $C$. But understanding these statements is extremely difficult without picking a complex structure on $C$ and using Hitchin's equations. We sketch the essential statements both for the ``unramified'' case that $C$ is a compact oriented two-manifold without boundary, and the ``ramified'' case that one allows punctures. We also give a few indications of why a more precise description requires a starting point in four-dimensional gauge theory.
Comments: 15 pp Subjects: Representation Theory (math.RT); Mathematical Physics (math-ph) Cite as: arXiv:0802.0999v1 [math.RT] Submission history From: Edward Witten [view email] [v1] Thu, 7 Feb 2008 16:11:53 GMT (18kb)
