The Fourier expansion of modular forms on quaternionic exceptional groups

2020/04/21 by Aaron Pollack · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Mathematical Identities

paper · doi:10.1215/00127094-2019-0063

Abstract

Suppose that G is a simple adjoint reductive group over Q, with an exceptional Dynkin type and with G(R) quaternionic (in the sense of Gross and Wallach). Then there is a notion of modular forms for G, anchored on the so-called quaternionic discrete series representations of G(R). The purpose of this paper is to give an explicit form of the Fourier expansion of modular forms on G, along the unipotent radical N of the Heisenberg parabolic P of G.

Cited by

• Gross's conjecture: the dihedral case
• Generalized Whittaker models beyond \mathfraksl₂-triples

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