Modular forms of half-integral weight on G_2

Aaron Pollack (UC San Diego)

Apr 14. 2022, 16:00 — 16:45

Modular forms of integral weight on G_2 and other exceptional groups were first studied by Gross-Wallach and Gan-Gross-Savin.  These are special automorphic forms that appear to behave similarly to classical holomorphic modular forms; they have a semi-classical notion of Fourier expansion and Fourier coefficients.  I will describe a theory of modular forms of half-integral weight on G_2 and other exceptional groups.  Moreover, using the automorphic minimal representation on F_4 (as studied by Loke-Savin and Ginzburg), we define a modular form of weight 1/2 on G_2 whose Fourier coefficients are related to the 2-torsion in the narrow class groups of totally real cubic fields.  This is joint work with Spencer Leslie.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Minimal Representations and Theta Correspondence (Workshop)
Wee Teck Gan (U of Singapore)
Marcela Hanzer (U Zagreb)
Alberto Minguez (U of Vienna)
Goran Muic (U Zagreb)
Martin Weissman (UC Santa Cruz)