A ${\mathrm{G}}_2$-period of a Fourier coefficient of an Eisenstein series on ${\mathrm{E}}_6$

Abstract

We calculate a ${\mathrm{G}}_2$-period of a Fourier coefficient of a cuspidal Eisenstein series on the split simply-connected group ${\mathrm{E}}_6$, and relate this period to the Ginzburg-Rallis period of cusp forms on ${\mathrm{GL}}_6$. This gives us a relation between the Ginzburg-Rallis period and the central value of the exterior cube L-function of ${\mathrm{GL}}_6$

30 pages