Suppose that is a simple adjoint reductive group over , with an exceptional Dynkin type and with quaternionic (in the sense of Gross and Wallach). Then there is a notion of modular forms for , anchored on the so-called quaternionic discrete series representations of . The purpose of this paper is to give an explicit form of the Fourier expansion of modular forms on , along the unipotent radical of the Heisenberg parabolic of .
"The Fourier expansion of modular forms on quaternionic exceptional groups." Duke Math. J. 169 (7) 1209 - 1280, 15 May 2020. https://doi.org/10.1215/00127094-2019-0063