Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New branching rules induced by plethysm   We derive group branching laws for formal characters of subgroups $H_\pi$ of
GL(n) leaving invariant an arbitrary tensor $T^\pi$ of Young symmetry type
$\pi$ where $\pi$ is an integer partition. The branchings $GL(n)\downarrow
GL(n-1)$, $GL(n)\downarrow O(n)$ and $GL(2n)\downarrow Sp(2n)$ fixing a vector
$v_i$, a symmetric tensor $g_{ij}=g_{ji}$ and an antisymmetric tensor
$f_{ij}=-f_{ji}$, respectively, are obtained as special cases. All new
branchings are governed by Schur function series obtained from plethysms of the
Schur function $s_\pi \equiv {\{} \pi {\}}$ by the basic $M$ series of complete
symmetric functions and the $L =M^{-1}$ series of elementary symmetric
functions. Our main technical tool is that of Hopf algebras, and our main
result is the derivation of a coproduct for any Schur function series obtained
by plethysm from another such series. Therefrom one easily obtains $\pi
$-generalized Newell-Littlewood formulae, and the algebra of the formal group
characters of these subgroups is established. Concrete examples and extensive
tabulations are displayed for $H_{1^3}$, $H_{21}$, and $H_{3}$, showing their
involved and nontrivial representation theory. The nature of the subgroups is
shown to be in general affine, and in some instances non reductive. We discuss
the complexity of the coproduct formula and give a graphical notation to cope
with it. We also discuss the way in which the group branching laws can be
reinterpreted as twisted structures deformed by highly nontrivial 2-cocycles.
The algebra of subgroup characters is identified as a cliffordization of the
algebra of symmetric functions for GL(n) formal characters. Modification rules
are beyond the scope of the present paper, but are briefly discussed.

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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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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: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: stat