Learn More
The indefinite orthogonal group G = O(p, q) has a distinguished infinite dimensional irreducible unitary representation π for p + q even and greater than 4, which is the " smallest " in the sense that the Gelfand–Kirillov dimension of π attains its (positive) minimum value p + q − 3 among the unitary dual of G. Moreover, π is the minimal representation if p(More)
We develop a theory of 'special functions' associated to a certain fourth order differential operator Dµ,ν on R depending on two parameters µ, ν. For integers µ, ν ≥ −1 with µ + ν ∈ 2N0 this operator extends to a self-adjoint operator on L 2 (R+, x µ+ν+1 dx) with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions,(More)
We introduce orthogonal polynomials M µ,ℓ j (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 L 2-model of the minimal unitary representations of indefinite orthogonal groups, and reduce to the classical Laguerre polynomials L µ(More)
  • 1