Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clebsch-Gordan coefficients of discrete groups in subgroup bases   We express each Clebsch-Gordan (CG) coefficient of a discrete group as a
product of a CG coefficient of its subgroup and a factor, which we call an
embedding factor. With an appropriate definition, such factors are fixed up to
phase ambiguities. Particularly, they are invariant under basis transformations
of irreducible representations of both the group and its subgroup. We then
impose on the embedding factors constraints, which relate them to their
counterparts under complex conjugate and therefore restrict the phases of
embedding factors. In some cases, the phase ambiguities are reduced to sign
ambiguities. We describe the procedure of obtaining embedding factors and then
calculate CG coefficients of the group \mathcal{PSL}_{2}\left(7\right) in terms
of embedding factors of its subgroups S_{4} and \mathcal{T}_{7}.

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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat