Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: W-graph determining elements in type A   Let $(W,S)$ be a Coxeter system of type $A$, so that $W$ can be identified
with the symmetric group $\mathrm{Sym}(n)$ for some positive integer $n$ and
$S$ with the set of simple transpositions $\{\,(i,i+1)\mid 1\leqslant
i\leqslant n-1\,\}$. Let $\leqslant_{\mathsf L}$ denote the left weak order on
$W$, and for each $J\subseteq S$ let $w_J$ be the longest element of the
subgroup $W_J$ generated by $J$. We show that the basic skew diagrams with $n$
boxes are in bijective correspondence with the pairs $(w,J)$ such that the set
$\{\,x\in W\mid w_J\leqslant_{\mathsf L} x\leqslant_{\mathsf L} ww_J\,\}$ is a
nonempty union of Kazhdan-Lusztig left cells. These are also the pairs $(w,J)$
such that $\mathscr{I}(w)=\{\,v\in W\mid v\leqslant_{\mathsf L} w\,\}$ is a
$W\!$-graph ideal with respect to $J$. Moreover, for each such pair the
elements of $\mathscr{I}(w)$ are in bijective correspondence with the standard
tableaux associated with the corresponding skew diagram.

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The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th