Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Horizontal Symmetry: Bottom Up and Top Down   A group-theoretical connection between horizontal symmetry $\G$ and fermion
mixing is established, and applied to neutrino mixing. The group-theoretical
approach is consistent with a dynamical theory based on $U(1)\times \G$, but
the dynamical theory can be used to pick out the most stable mixing that purely
group-theoretical considerations cannot. A symmetry common to leptons and
quarks is also discussed. This higher symmetry picks $A_4$ over $S_4$ to be the
preferred symmetry for leptons.

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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
3
The categories of this paper are: physics