Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes on affine isometric actions of discrete groups   Consider a lattice $\Gamma$ in a group $G = SL_2(\R), SO(1,n), SU(1,n)$,
$SL_2(\Q_p)$. We discuss actions of $\Gamma$ by affine isometric
transformations of Hilbert spaces. We show that for irreducible affine
isometric action of $G$ its restriction to $\Gamma$ is irreducible. We prove
the existence of canonical irreducible affine isometric actions of $\Gamma$
associated to actions of $\Gamma$ on $\R$- trees. Using such actions we
construct irreducible representations of semigroup of probabilistic measures on
$\Gamma$ and construct the series of representations of the groups of
diffeomorphisms of Riemann surfaces enumerated by the points of Thurston
compactification of Teichm\"uller (Teichmuller) space.

9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph