Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallelotope tilings and $q$-decomposition numbers   We provide closed formulas for a large subset of the canonical basis vectors
of the Fock space representation of $U_q(\widehat{\mathfrak{sl}}_e)$. These
formulas arise from parallelotopes which assemble to form polytopal complexes.
The subgraphs of the $\mathrm{Ext}^1$-quivers of $v$-Schur algebras at complex
$e$-th roots of unity generated by simple modules corresponding to these
canonical basis vectors are given by the $1$-skeletons of the polytopal
complexes.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn