On the Weyl Representation of Metaplectic Operators

On the Weyl Representation of Metaplectic Operators

Abstract. 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 Maslovtype indices; these indices intervene in a crucial way in Gutzwiller’s formula of semiclassical mechanics, and are simply related to a...

On the Mehlig-wilkinson Representation of Metaplectic Operators

We study the Weyl representation of metaplectic operators suggested by earlier work of Mehlig and Wilkinson. We give precise calculations for the associated Maslov indices; these intervene in a crucial way in the Gutzwiller formula of semiclassical mechanics.

METAPLECTIC OPERATORS ON C n by HANS

The metaplectic representation describes a class of automorphisms of the Heisenberg group H = H(G), defined for a locally compact abelian groupG. ForG = R ,H is the usual Heisenberg group. For the case when G is the finite cyclic group Zn, only partial constructions are known. Here we present new results for this case and we obtain an explicit construction of the metaplectic operators on C. We ...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

On the Number of Local Newforms in a Metaplectic Representation

The nonarchimedean local analogues of modular forms of half-integral weight with level and character are certain vectors in irreducible, admissible, genuine representations of the metaplectic group over a nonarchimedean local field of characteristic zero. Two natural level raising operators act on such vectors, leading to the concepts of oldforms and newforms. We prove that the number of newfor...