Automorphic representations of small nilpotent orbits, BPS conditions and new automorphic functions
Event details
| Date | 26.11.2014 |
| Hour | 15:15 › 16:15 |
| Speaker | Pierre Vanhove |
| Location | |
| Category | Conferences - Seminars |
Maximally supersymmetric string theory compactified on (d—1)-dimensional torus (1<=d<=8) is invariant under U-duality groups G_d(Z)\ G_d/K_d where G_d is the real split form of the simply laced lie group of rank d and K_d is the maximal compact subgroup. The connection between string theory compactified on tori of various dimensions naturally leads to the nested structure where lower rank G_d appear as parabolic subgroup of E8 which describes string theory in three dimensions. Scattering amplitudes in string theory lead to automorphic functions under G_d(Z). Conditions from string theory allow to derive the laplace equation satisfied by these functions, and for well choosen maximal parabolic subgroups the constant terms. As well, the support of the non-vanishing Fourier coefficients are determined by conditions from supersymmetry BPS conditions and correspond to nilpotent character variety orbits. In this talk we will provide an explicit construction of these automorphic functions. We will show that the wavefront sets of these automorphic forms are supported on only certain coadjoint nilpotent orbits: just the minimal and trivial orbits in the first non-trivial case, and just the next-to-minimal, minimal and trivial orbits in the second non-trivial case. Thus the next-to-minimal representations occur automorphically for E6, E7, and E8, and hence the first two nontrivial low energy coefficients in scattering amplitudes can be thought of as exotic Theta-functions for these groups. We will show that these automorphic representations are residues of Eisenstein series. We will detail the arguments that the automorphic representations attached to next nilpotent orbits in the Hasse diagram are not Eisenstein series. For the case of SL(2,Z), we will provide a complete construction of this new automorphic function using Eisenstein automorphic distributions. This is based on the work done with Michael B. Green, Stephen D. Miller, Jorge G. Russo,[arXiv:1004.0163] Michael B. Green, Stephen D. Miller, [arXiv:1111.2983] Michael B. Green, Stephen D. Miller,[arXiv:1404.2192]
Practical information
- Informed public
- Free
Organizer
- Natascha Fontana