The inversion formula and holomorphic extension of the minimal representation of the conformal group

By Toshiyuki Kobayashi, Gen Mano. 2006

66 citations recorded by the source corpus.

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 m with respect to the measure |x| 1 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 m,1 .

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/72f9252b556cb0f900f276e6f36e45c6ed8ab604

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In Applied Mathematics

1. Hendrik De Bie
2. Nele De Schepper
3. F. Sommen
4. Irene Sabadini
5. Fabrizio Colombo
6. Hennie De Schepper

In Mathematical Physics

1. Nele De Schepper
2. F. Sommen
3. Hendrik De Bie
4. Irene Sabadini
5. Fabrizio Colombo

Citations in the corpus

• The Class of Clifford-Fourier Transforms (2011, methodology): “This formulation stems from representation theory (see [19, 20]) and has been used in recent work on minimal representations (see [21, 22] and further generalizations in [1]).”