Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic quotients of the mapping class group   To every $Q$-irreducible representation $r$ of a finite group $H$, there
corresponds a simple factor $A$ of $Q[H]$ with an involution $\tau$. To this
pair $(A,\tau)$, we associate an arithmetic group $\Omega$ consisting of all
$(2g-2)\times (2g-2)$ matrices over a natural order of $A^{op}$ which preserve
a natural skew-Hermitian sesquilinear form on $A^{2g-2}$. We show that if $H$
is generated by less than $g$ elements, then $\Omega$ is a virtual quotient of
the mapping class group $Mod(\Sigma_g)$, i.e. a finite index subgroup of
$\Omega$ is a quotient of a finite index subgroup of $\Mod(\Sigma_g)$. This
shows that the mapping class group has a rich family of arithmetic quotients
(and "Torelli subgroups") for which the classical quotient $Sp(2g, Z)$ is just
a first case in a list, the case corresponding to the trivial group $H$ and the
trivial representation. Other pairs of $H$ and $r$ give rise to many new
arithmetic quotients of $Mod(\Sigma_g)$ which are defined over various
(subfields of) cyclotomic fields and are of type $Sp(2m), SO(2m,2m),$ and
$SU(m,m)$ for arbitrarily large $m$.

18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th