d-Orthogonal polynomials and su(2)

Two families of d-orthogonal polynomials related to su(2) are identified and studied. The algebraic setting allows for their full characterization (explicit expressions, recurrence relations, difference equations, generating functions, etc.). In the limit where su(2) contracts to the Heisenberg–Weyl algebra h1, the polynomials tend to the standard Meixner polynomials and d-Charlier polynomials, respectively.