Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiplier systems for Hermitian modular groups   Let $\Gamma_{F,n}$ be the Hermitian modular group of degree $n>1$ in sense of
Hel Braun with respect to an imaginary quadratic field $F$. Let $r$ be a
natural number. There exists a multiplier system of weight $1/r$ (equivalently
a Hermitian modular form of weight $k+1/r$, $k$ integral) on some congruence
group if and only if $r=1$ or $2$. This follows from a much more general
construction of Deligne [De] combining it with results of Hill [Hi], Prasad [P]
and Prasad-Rapinchuk [PR]. As far as we know, the systems of weight $1/2$ have
not yet been described explicitly. Remarkably Haowu Wang [Wa] gave an example
of a modular form of half integral weight. Actually he constructs a Borcherds
product of weight $23/2$ for a group of type $O(2,4)$. This group is isogenous
to the group $U(2,2)$ that contains the Hermitian modular groups of degree two.
In this paper we want to study such multiplier systems. If one restricts them
to the unimodular group one obtains a usual character. Our main result states
that the kernel of this character is a non-congruence subgroup. For
sufficiently small $\Gamma$ it coincides with the group described by Kubota in
the case $n=2$ and by Bass Milnor Serre in the case $n>2$.

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The categories of this paper are: econ
28
The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat