Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free product formulae for quantum permutation groups   Associated to a finite graph $X$ is its quantum automorphism group $G(X)$. We
prove a formula of type $G(X*Y)=G(X)*_wG(Y)$, where $*_w$ is a free wreath
product. Then we discuss representation theory of free wreath products, with
the conjectural formula $\mu (G*_wH)=\mu (G)\boxtimes\mu (H)$, where $\mu$ is
the associated spectral measure. This is verified in two situations: one using
free probability techniques, the other one using planar algebras.

4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin