Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distance-regular graphs and the $q$-tetrahedron algebra   Let $\Gamma$ denote a distance-regular graph with classical parameters
$(D,b,\alpha,\beta)$ and $b\not=1$, $\alpha=b-1$. The condition on $\alpha$
implies that $\Gamma$ is formally self-dual. For $b=q^2$ we use the adjacency
matrix and dual adjacency matrix to obtain an action of the $q$-tetrahedron
algebra $\boxtimes_q$ on the standard module of $\Gamma$. We describe four
algebra homomorphisms into $\boxtimes_q$ from the quantum affine algebra
$U_q({\hat{\mathfrak{sl}}_2})$; using these we pull back the above
$\boxtimes_q$-action to obtain four actions of $U_q({\hat{\mathfrak{sl}}_2})$
on the standard module of $\Gamma$.

15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin