Explicit realization of a higher metaplectic representation

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 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...

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.

Realization of Analysis into Explicit Mathematics

We define a novel interpretation R of second order arithmetic into Explicit Mathematics. As a difference from standard D-interpretation, which was used before and was shown to interpret only subsystems proof-theoretically weaker than T0, our interpretation can reach the full strength of T0. The R-interpretation is an adaptation of Kleene’s recursive realizability, and is applicable only to intu...

Feynman path integrals on phase space and the metaplectic representation