Integral Formulas for the Minimal Representation of O(p,2)

The minimal representation of O(p,q) (p+q: even) is realized on the Hilbert space of square integrable functions on the conical subvariety of R^p+q–2. This model presents a close resemblance of the Schrödinger model of the Segal–Shale–Weil representation of the metaplectic group. We shall give explicit integral formulas for the inversion together with the analytic continuation to a certain semigroup of O(p+2,C) of the minimal representation of O(p,2) by using Bessel functions.Mathematics Subject Classifications (2000) primary 22E30; secondary 22E46, 20M20, 43A80.