The minimal representation π of O(p, q) (p+q: even) is realized on the Hilbert space of square integrable functions on the conical subvariety of Rp+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.
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© Toshiyuki Kobayashi