Automorphic realizations of small representations and graviton scattering

Automorphic realizations of minimal representations have been useful in several number-theoretic constructions, including L-function constructions and instances of Langlands functoriality. I’ll describe the appearance of some of these exotic theta-functions – as well as some previously undiscovered ones on E7 and E8 – in the low energy expansion of graviton scattering amplitudes. The constructions establish some new cases of Arthur’s conjectures on unipotent representations, and in particular give a number of new examples of unitary representations of exceptional groups. (Joint work with Michael B. Green and Pierre Vanhove)