Representations of the Schrödinger group and matrix orthogonal polynomials

Abstract

The representations of the Schrödinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable that have Charlier and Meixner polynomials as building blocks. The underlying Lie-theoretic framework allows for a systematic derivation of the structural formulas (recurrence relations, difference equations, Rodrigues' formula etc.) that these matrix orthogonal polynomials satisfy.

33 pages

References in corpus (2)

• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• The Analytic Theory of Matrix Orthogonal Polynomials

Cited by in corpus (7)

• The multivariate Charlier polynomials as matrix elements of the Euclidean group representation on oscillator states
• Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials
• An Algebraic Model for the Multiple Meixner Polynomials of the First Kind
• Dynamical Invariants and Berry's Phase for Generalized Driven Harmonic Oscillators
• Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras
• The Berry Phase for Simple Harmonic Oscillators
• On a Hidden Symmetry of Quantum Harmonic Oscillators