Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hopf algebras and characters of classical groups   Schur functions provide an integral basis of the ring of symmetric functions.
It is shown that this ring has a natural Hopf algebra structure by identifying
the appropriate product, coproduct, unit, counit and antipode, and their
properties. Characters of covariant tensor irreducible representations of the
classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur
functions, and the Hopf algebra is exploited in the determination of
group-subgroup branching rules and the decomposition of tensor products. The
analysis is carried out in terms of n-independent universal characters. The
corresponding rings, CharGL, CharO and CharSp, of universal characters each
have their own natural Hopf algebra structure. The appropriate product,
coproduct, unit, counit and antipode are identified in each case.

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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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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: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org