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Hofstadter's Butterfly and Langlands Duality (1708.00436v1)
Published 27 Jul 2017 in cond-mat.mes-hall, hep-th, math-ph, and math.MP
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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