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Langlands correspondence and integrable systems

Le : 06/02/2008 14h15
Par : Alexander CHERVOV (LAREMA and Moscow ITEP)
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Résumé : The geometric version of the Langlands correspondence relates representations of certain infinite-dimensional Lie algebra and differential operators in one variable. The analogy between the arithmetic version can be seen via identification of Galois group with fundamental group and reprsentations of the fundamental group with monodromies of the differential operators. We present a simple construction of the correspondence based on explicit formula for the generators of the center of the universal enveloping of affine Lie algebra (\hat gl_n)$. The applications to the theory of integrable systems will be explained.