Hofstadter’s butterfly and Langlands duality

Kazuki Ikeda

Type: Article

Publication Date: 2018-06-01

Citations: 16

DOI: https://doi.org/10.1063/1.4998635

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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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Journal of Mathematical Physics - View
arXiv (Cornell University) - View - PDF
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