Electron. J. Diff. Equ., Vol. 2015 (2015), No. 260, pp. 1-28.

A system of Schrodinger equations and the oscillator representation

Markus Hunziker, Mark R. Sepanski, Ronald J. Stanke

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.

Submitted October 4, 2013. Published October 7, 2015.
Math Subject Classifications: 22E30, 35A30, 35J10, 58J70.
Key Words: Oscillator representation; Schrodinger equation; metaplectic representation; Segal-Shale-Weil representation; Jacobi group.

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Markus Hunziker
Department of Mathematics
Baylor University
One Bear Place 97328
Waco, TX 76798-7328, USA
email: Markus_Hunziker@baylor.edu
Mark R. Sepanski
Department of Mathematics
Baylor University
One Bear Place 97328
Waco, TX 76798-7328, USA
email: Mark_Sepanski@baylor.edu
Ronald J. Stanke
Department of Mathematics
Baylor University
One Bear Place 97328
Waco, TX 76798-7328, USA
email: Ronald_Stanke@baylor.edu

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