Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The inversion formula and holomorphic extension of the minimal
  representation of the conformal group   The minimal representation $\pi$ of the indefinite orthogonal group
$O(m+1,2)$ is realized on the Hilbert space of square integrable functions on
$\mathbb R^m$ with respect to the measure $|x|^{-1} dx_1... dx_m$.
  This article gives an explicit integral formula for the holomorphic extension
of $\pi$ to a holomorphic semigroup of $O(m+3, \mathbb C)$ 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 $\mathbb R^{m,1}$.

7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat