The inversion formula and holomorphic extension of the minimal representation of the conformal group
نویسنده
چکیده
The minimal representation π of the indefinite orthogonal group O(m+ 1, 2) is realized on the Hilbert space of square integrable functions on R with respect to the measure |x|dx1 · · ·dxm. This article gives an explicit integral formula for the holomorphic extension of π to a holomorphic semigroup of O(m + 3,C) by means of the Bessel function. Taking its ‘boundary value’, we also find the integral kernel of the ‘inversion operator’ corresponding to the inversion element on the Minkowski space R. Mathematics Subject Classifications (2000) : Primary 22E30; Secondary 22E45, 33C10 35J10, 43A80, 43A85, 47D05, 51B20.
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