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

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

2009-07-19

arxiv.org/abs/0907.3266v1

Mathematics

Quantum Algebra

Latex, 26 pages

Scientific paper

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.

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