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Three sides of the geometric Langlands correspondence for gl_N Gaudin model and Bethe vector averaging maps

Research paper by E. Mukhin, V. Tarasov, A. Varchenko

Indexed on: 19 Jul '09Published on: 19 Jul '09Published in: Mathematics - Quantum Algebra



Abstract

We consider the gl_N Gaudin model of a tensor power of the standard vector representation. The geometric Langlands correspondence in the Gaudin model relates the Bethe algebra of the commuting Gaudin Hamiltonians and the algebra of functions on a suitable space of N-th order differential operators. In this paper we introduce a third side of the correspondence: the algebra of functions on the critical set of a master function. We construct isomorphisms of the third algebra and the first two. A new object is the Bethe vector averaging maps.