Poles, Residues and Siegel-Weil Identities of Degenerate Eisenstein Series on Split Exceptional Groups of Type $E_n$

Hezi Halawi, Hebrew University, Rehovot, Israel, and Avner Segal, Shamoon College of Engineering, Beer-Sheva, Israel

Chapters Introduction 1. Preliminaries 1. Background Theory 2. Split Exceptional Groups of Type $E_n$ 3. Local Degenerate Principal Series 4. Assumptions Made Throughout This Paper 2. The Degenerate Residual Spectrum of Groups of Type $E_n$ 5. Poles of Degenerate Eisenstein Series 6. Square-Integrable Degenerate Residual Spectrum 7. Siegel-Weil Identities 8. Arthur Parameters of the Square-Integrable Degenerate Residual Representations 9. Non-Square-Integrable Degenerate Residual Spectrum A. Appendices A. Local Calculations