The Pseudo-Character of the Weil Representation and its Relation with the Conley-Zehnder Index.

link: http://arxiv.org/abs/0909.1437
Abstract

We calculate the character of the Weil representation using previous results
which express the Weyl symbol of metaplectic operators in terms of the
symplectic Cayley transform and the Conley--Zehnder index.