Finite Quantum Oscillator and Matrix Multi-Orthogonality

Matrix multi-orthogonal polynomials generalise the standard orthogonal polynomials in that they are matrices of polynomials which obey higher recurrence relations. These polynomials were introduced almost 20 years ago notably by Van Assche,Van Iseghem, Sorokin and others in the context of simultaneous Padé approximation. Recently (Vinet/Zhedanov-2011), matrix orthogonality has appeared in the context of the representations of the Schrödinger group and Coherent/Squeezed states of the quantum oscillator. In this talk, I will discuss how multi-orthogonality arises in the context of a discrete quantum oscillator model due to Wolf et al. and its Coherent/Squeezed-like states.