Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-Dimensional Irreducible Modules of the Racah Algebra at
  Characteristic Zero   Assume that ${\mathbb F}$ is an algebraically closed field with
characteristic zero. The Racah algebra $\Re$ is the unital associative
${\mathbb F}$-algebra defined by generators and relations in the following way.
The generators are $A$, $B$, $C$, $D$ and the relations assert that
$[A,B]=[B,C]=[C,A]=2D$ and that each of $[A,D]+AC-BA$, $[B,D]+BA-CB$,
$[C,D]+CB-AC$ is central in $\Re$. In this paper we discuss the
finite-dimensional irreducible $\Re$-modules in detail and classify them up to
isomorphism. To do this, we apply an infinite-dimensional $\Re$-module and its
universal property. We additionally give the necessary and sufficient
conditions for $A$, $B$, $C$ to be diagonalizable on finite-dimensional
irreducible $\Re$-modules.

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph