We study the Weyl representation of metaplectic operators associated to a
symplectic matrix having no non-trivial fixed point, and justify a formula
suggested in earlier work of Mehlig and Wilkinson. We give precise calculations
of the associated Maslov-type indices; these indices intervene in a crucial way
in Gutzwiller's formula of semiclassical mechanics, and are simply related to
an index defined by Conley and Zehnder.Comment: To appear in Lett. Math. Physiqu

De Gosson, Maurice