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SUMMARY:Automorphic representations of small nilpotent orbits\, BPS condit
 ions and new automorphic functions 
DTSTART:20141126T151500
DTEND:20141126T161500
DTSTAMP:20260415T024339Z
UID:eb4363a6b71b7b531b2a0419236054792716a277685f20af4e10024f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Pierre Vanhove\nMaximally supersymmetric string theory compact
 ified 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 l
 aced lie group of rank d and K_d is the maximal compact subgroup. The conn
 ection between  string theory compactified on tori of various dimensions 
 naturally leads  to the nested structure where lower rank G_d appear as p
 arabolic subgroup of E8 which describes string theory in three dimensions.
   Scattering amplitudes in string theory lead to automorphic functions un
 der G_d(Z).  Conditions from string theory allow to derive the laplace eq
 uation satisfied by these functions\, and for well choosen maximal parabol
 ic subgroups the constant terms. As well\, the support of the non-vanishin
 g Fourier coefficients are determined by conditions from supersymmetry BPS
  conditions and correspond to nilpotent character variety orbits.  In thi
 s talk we will provide an explicit construction of these automorphic funct
 ions. We will show that  the wavefront sets of these automorphic forms ar
 e supported on only certain coadjoint nilpotent orbits: just the minimal a
 nd trivial orbits in the first non-trivial case\, and just the next-to-min
 imal\, minimal and trivial orbits in the second non-trivial case. Thus  t
 he next-to-minimal representations occur automorphically for E6\, E7\, and
  E8\, and hence the first two nontrivial low energy coefficients in scatte
 ring amplitudes can be thought of as exotic Theta-functions for these grou
 ps.  We will show that these automorphic representations are residues of 
 Eisenstein series.  We will detail the arguments that the  automorphic r
 epresentations attached to next nilpotent orbits in the Hasse diagram  ar
 e not Eisenstein series. For the case of SL(2\,Z)\, we will provide a comp
 lete construction of this new automorphic function using Eisenstein automo
 rphic distributions.  This is based on the work done with  Michael B. Gr
 een\, Stephen D. Miller\, Jorge G. Russo\,[arXiv:1004.0163] Michael B. Gre
 en\, Stephen D. Miller\, [arXiv:1111.2983] Michael B. Green\, Stephen D. M
 iller\,[arXiv:1404.2192]
LOCATION:MA 30 http://plan.epfl.ch/?lang=fr&room=MA30
STATUS:CONFIRMED
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