Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Verma Modules over a ${\mathbb Z}_2 \otimes {\mathbb Z}_2$ Graded
  Superalgebra and Invariant Differential Equations   Lowest weight representations of the ${\mathbb Z}_2 \otimes {\mathbb Z}_2$
graded superalgebra introduced by Rittenberg and Wyler are investigated. We
give a explicit construction of Verma modules over the ${\mathbb Z}_2 \otimes
{\mathbb Z}_2$ graded superalgebra and show their reducibility by using
singular vectors. The explicit formula of singular vectors are given and are
used to derive partial differential equations invariant under the color
supergroup generated by the ${\mathbb Z}_2 \otimes {\mathbb Z}_2$ graded
superalgebra.

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The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph