Finite Quadratic Modules and Weil Representations over Number FieldsSpeaker: Hatice Boylan (MPIM)
Time: 4.00 PM
Date: Thursday February 7th 2013
Location: Mathematics Seminar Room, Room AG 1.01, First Floor, Agriculture Building, UCD Belfield
In the study of Hilbert, Jacobi and orthogonal modular forms of low weight over number fields it is essential to understand the representations of Hilbert modular groups or of certain two-fold central extensions. In the case of the field of natural numbers it is known that the key to the study of all representations of the modular group SL(2,Z) which are interesting in the mentioned context are the Weil representations associated to finite quadratic modules. In analogy to the case of the field of rational numbers we developed a theory of finite quadratic modules and their associated Weil representations over arbitrary number fields. In this talk we report about the main features of this new theory, about interesting new phenomena arising in the general theory over arbitrary number fields, and we indicate applications to the explicit construction of automorphic forms over number fields.