Hofstadter's Butterfly and Langlands Duality
arXiv:1708.00436 · doi:10.1063/1.4998635
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".
9 pages, 1 figure