Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distance-regular graphs of $q$-Racah type and the universal Askey-Wilson
  algebra   Let $\C$ denote the field of complex numbers, and fix a nonzero $q \in \C$
such that $q^4 \ne 1$. Define a $\C$-algebra $\Delta_q$ by generators and
relations in the following way. The generators are $A,B,C$. The relations
assert that each of $A+\frac{qBC-q^{-1}CB}{q^2-q^{-2}}$,
$B+\frac{qCA-q^{-1}AC}{q^2-q^{-2}}$, $C+\frac{qAB-q^{-1}BA}{q^2-q^{-2}}$ is
central in $\Delta_q$. The algebra $\Delta_q$ is called the universal
Askey-Wilson algebra. Let $\Gamma$ denote a distance-regular graph that has
$q$-Racah type. Fix a vertex $x$ of $\Gamma$ and let $T=T(x)$ denote the
corresponding subconstituent algebra. In this paper we discuss a relationship
between $\Delta_q$ and $T$. Assuming that every irreducible $T$-module is thin,
we display a surjective $\C$-algebra homomorphism $\Delta_q \to T$. This gives
a $\Delta_q$ action on the standard module of $T$.

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The categories of this paper are: cs
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: stat