Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensorial generalization of characters   In rainbow tensor models, which generalize rectangular complex matrix model
(RCM) and possess a huge gauge symmetry $U(N_1)\times\ldots\times U(N_r)$, we
introduce a new sub-basis in the linear space of gauge invariant operators,
which is a redundant basis in the space of operators with non-zero Gaussian
averages. Its elements are labeled by $r$-tuples of Young diagrams of a given
size equal to the power of tensor field. Their tensor model averages are just
products of dimensions: $\Big<\chi_{R_1,\ldots,R_r}\Big> \sim C_{R_1,\ldots,
R_r}D_{R_1}(N_1)\ldots D_{R_r}(N_r)$ of representations $R_i$ of the linear
group $SL(N_i)$, with $C_{R_1,\ldots, R_r}$ made of the Clebsch-Gordan
coefficients of representations $R_i$ of the symmetric group. Moreover, not
only the averages but the operators $\chi_{\vec R}$ themselves exist only when
these $C_{\vec R}$ are non-vanishing. This sub-basis is much similar to the
basis of characters (Schur functions) in matrix models, which is distinguished
by the property $\Big<{\rm character}\Big> \sim { character}$, which opens a
way to lift the notion and the theory of characters (Schur functions) from
matrices to tensors. In particular, operators $\chi_{\vec R}$ are
eigenfunctions of operators which generalize the usual cut-and-join operators
$\hat W$; they satisfy orthogonality conditions similar to the standard
characters, but they do not form a {\it full} linear basis for all
gauge-invariant operators, only for those which have non-vanishing Gaussian
averages.

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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom