Hofstadter's Butterfly and Langlands Duality

Kazuki Ikeda

doi:10.1063/1.4998635

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arXiv · 1708.00436

Hofstadter's Butterfly and Langlands Duality

Kazuki Ikeda

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Abstract

We dig out a deeper mathematical structure of the quantum Hall system from a perspective of the Langlands program. An algebraic expression of the Hamiltonian with the quantum group is a cornerstone. The Langlands duality of the quantum group sheds light on the fractal structure of Hofstadter's butterfly. This would imply a "quantum Langlands duality".

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Kazuki Ikeda. 2017-07-27. Hofstadter's Butterfly and Langlands Duality. https://doi.org/10.1063/1.4998635

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