BIRS Workshop Lecture Videos
Automorphic representations, Whittaker vectors, and black holes Persson, Daniel
Automorphic forms on exceptional Lie groups appear naturally in string theory compactifications. They manifest themselves as couplings in higher derivative corrections and in terms of generating functions of black hole microstates. I will demonstrate how certain Fourier coefficients attached to the minimal automorphic representations of $E_6$, $E_7$, and $E_8$ are determined by maximally degenerate Whittaker vectors. This fact allows for a simple method for calculating explicit Fourier coefficients which are relevant in string theory. Various recent results, conjectures and open problems are outlined.
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