We introduce orthogonal polynomials Mjμ,l(x) as eigenfunctions of a certain self-adjoint fourth order differential operator depending on two parameters μ ∈ C and l ∈ N0. These polynomials arise as K-finite vectors in the L2-model of the minimal unitary representations of indefinite orthogonal groups, and reduce to the classical Laguerre polynomials Ljμ(x) for l = 0. We establish various recurrence relations and integral representations for our polynomials, as well as a closed formula for the L2-norm. Further we show that they are uniquely determined as polynomial eigenfunctions.
© Toshiyuki Kobayashi