Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Splitting the square of homogeneous and elementary functions into their
  symmetric and anti-symmetric parts   We consider the expansion of the square of a complete homogeneous function
$h_\lambda$, or of an elementary symmetric function $e_\lambda$, in the basis
of Schur functions. This square also decomposes into two plethysms,
$s_2[h_\lambda]$ and $s_{11}[h_\lambda]$ (resp. $s_2[h_\lambda]$ and
$s_{11}[h_\lambda]$), which are called its symmetric and anti-symmetric parts,
respectively. We define a sign statistic on the set of tableaux that index the
Schur functions appearing in the square of those symmetric functions. This sign
statistic allows to determine to which plethysm each Schur function
contributes. We use mainly combinatorial tools on tableaux (product on tableau
and RSK) and basic manipulations on plethysm and symmetric functions.

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The categories of this paper are: hep-ex
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The categories of this paper are: physics
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th