Abstract
These are three introductory lectures on the relation between representations of affine Kac-Moody algebras, homology of configuration spaces with local coefficient systems, and quantum groups. The first lecture contains background on highest weight representations of affine Kac-Moody algebras. In the second lecture, conformal blocks, the Friedan-Shenker connection and the Knizhnik-Zamolodchikov (KZ) equation are reviewed. In the third lecture, the case of sl z is studied in more detail. Integral representations of solutions of the KZ equation are derived, and recent results, obtained in collaboration with C. Wieczerkowski, on the relation between integration cycles and representations of U q (sl 2) are explained.
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