SEMPARIS – Séminaires en région parisienne Séminaire Groupes

SEMPARIS – S´eminaires en r´egion parisienne
http ://string.lpthe.jussieu.fr/semparis/
S´ eminaire Groupes R´ eductifs et Formes
Automorphes
Jeudi 5 Juillet 2012, 14 :30
IM-JUSSIEU-PRG, 15-16-417 `a Jussieu
Domaines : math.GR
Titre : The Second Term Identity of the regularised siegel-Weil formula
Orateur : Wee Teck Gan ( University of Singapore )
R´esum´e : Kudla and Rallis inititaed the subject of the regularized Siegel-Weil
formula for its application to the Rallis inner product formula. The purpose
of the regularized Siegel-Weil formula is to relate a regularized theta integral
to a Siegel-Eisenstein series. For symplectic groups, they proved an iden-
tity (called the first term identity) between the leading terms of the Laurent
expansion of the two sides, and this was subsequently extended to other clas-
sical groups by others. Such a first term identtiy is sufficient for the Rallis
inner product formula in certain situations. In this talk, we discussed joint
work with Yannan Qiu and Shuichiro Takeda in which we proved the general
second term identity which relates the next terms in the Laurent expansion.
This second term identity is necessary to establish the Rallis inner product
formula in the remaining situations.