Hecke Operators (Part One)
David Ben-Zvi (The University of Texas at Austin)
April 12th, 2007 at University of Oxford
Special thanks to Charles Beesley, Head of Media Production, University of Oxford
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Abstract:
What acts on functions on a quotient space, or on spaces of invariant functions? A general answer is provided by Hecke algebras. We'll investigate the symmetries of the geometric Langlands function spaces through the study of the affine Grassmannian. Miraculously, the Hecke operators we encounter all commute, and the geometric Langlands program emerges naturally as an attempt to simultaneously diagonalize commuting Hecke operators. The geometric origin of the commutativity will also be profitably linked to the notion of a vertex algebra.