Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Connection between Easy Quantum Groups, Varieties of Groups and
  Reflection Groups   We present a link between easy quantum groups, discrete groups and
combinatorics. By this, we infer new connections between quantum isometry
groups, reflection groups, varieties of groups and the combinatorics of
partitions. More precisely, we consider easy quantum groups and find a relation
to subgroups of the infinite free product $\mathbb Z_2^{*\infty}$ of $\mathbb
Z_2=\mathbb Z/2\mathbb Z$. We obtain a link with reflection groups and thus
with varieties of groups, which yields a statement on the complexity of the
class of easy quantum groups on the one hand, and a "quantum invariant" for
varieties of groups on the other hand. Moreover, we reveal a triangular
relationship between easy quantum groups, categories of partitions and discrete
groups (reflection groups). As a by-product, we obtain a large number of new
quantum isometry groups.

24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
3
The categories of this paper are: physics