A system of Schrodinger equations and the oscillator representation

Abstract

We construct a copy of the oscillator representation of the metaplectic group Mp(n) in the space of solutions to a system of Schrodinger type equations on $\mathbb{R}^{n}\times\hbox{Sym}(n,\mathbb{R})$ that has very simple intertwining maps to the realizations given by Kashiwara and Vergne.

Keywords

• Oscillator representation
• Schrodinger equation
• metaplectic representation
• Segal-Shale-Weil representation
• Jacobi group