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arXiv · 1707.07873

Quantisation conditions of the quantum Hitchin system and the real geometric Langlands correspondence

Joerg Teschner
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Abstract

Single-valuedness of the eigenfunctions of the quantised Hitchin Hamiltonians is proposed as a natural quantisation condition. Separation of Variables can be used to relate the classification of eigenstates to the classification of projective structures with real holonomy. Using complex Fenchel-Nielsen coordinates one may reformulate the quantisation conditions in terms of the generating function for the variety of opers. These results are interpreted as a variant of the geometric Langlands correspondence.

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Joerg Teschner. 2017-07-25. Quantisation conditions of the quantum Hitchin system and the real geometric Langlands correspondence. https://arxiv.org/abs/1707.07873

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