On spectral analysis of a magnetic Schrodinger operator on planar mixed automorphic forms

We characterize the space of the so-called planar mixed automorphic forms of type $(\nu ,\mu )$ with respect to an equivariant pair $(\rho ,\tau )$ as the image of the usual automorphic forms by an appropriate transform and we investigate some concrete basic spectral properties of a magnetic Schrodinger operator acting on them. The associated polynomials constitute classes of generalized complex polynomials of Hermite type.