The inversion formula and holomorphic extension of the minimal representation of the conformal group
The inversion formula and holomorphic extension of the minimal representation of the conformal group
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DOI：
10.1142/9789812770790_0006
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发表时间：
2006-06
期刊：
影响因子：
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通讯作者：
Toshiyuki Kobayashi;Gen Mano
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文献类型：
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作者：
Toshiyuki Kobayashi;Gen Mano
不定正交群O（m +1，2）的极小表示π在Rm上平方可积函数的Hilbert空间上关于测度实现|X| 1 dx1 � � dxm.利用Bessel函数给出了π到O（m + 3，C）的全纯半群的全纯扩张的一个显式积分公式.取其“边界值”，我们还找到了与Minkowski空间Rm，1上的反演元素相对应的“反演算子”的积分核。
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 .