Ebook: The Weil representation, Maslov index and Theta series

* A collection of research-oriented monographs, reports, notes arising from lectures or seminars

* Quickly published concurrent with research

* Easily accessible through international distribution facilities

* Reasonably priced

* Reporting research developments combining original results with an expository treatment of the particular subject area

* A contribution to the international scientific community: for colleagues and for graduate students who are seeking current information and directions in their graduate and post-graduate work

---

In these notes, the Shale-Weil representation of the symplectic group is discussed, as well as some of its applications to number theory. The monograph is composed of two parts: In Part I, written by Gerard Lion and Michele Vergne, we introduce the Shale-Weil representation and establish a relation between its cocycle and the Maslov index. In Part II, written by Michele Vergne, applications of e-series to liftings of modular forms are given. Although the results of the first part enlightens the exposition of the classical transformation properties of e-functions, a reader mainly interested by these applications to liftings could read directly the second part with an eventual glance to earlier paragraphs. The two parts have separate introductions and bibliographical notes.