On Concrete Spectral Properties of a Twisted Laplacian Associated with a Central Extension of the Real Heisenberg Group

Abstract

We consider the special magnetic Laplacian given by Δν,μ=4∑j=1n∂2/∂zj∂zj¯+2iνE+E¯+n+2μE-E¯-ν2+μ2z2. We show that Δν,μ is connected to the sub-Laplacian of a group of Heisenberg type given by C ×ω Cn realized as a central extension of the real Heisenberg group H2n+1. We also discuss invariance properties of Δν,μ and give some of their explicit spectral properties.