Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free quantum analogue of Coxeter group $D_4$   We define the quantum group $D_4^+$ -- a free quantum version of the
demihyperoctahedral group $D_4$ (the smallest representative of the Coxeter
series $D$). In order to do so, we construct a free analogue of the property
that a $4\times4$ matrix has determinant one. Such analogues of determinants
are usually very hard to define for free quantum groups in general and our
result only holds for the matrix size $N=4$. The free $D_4^+$ is then defined
by imposing this generalized determinant condition on the free hyperoctahedral
group $H_4^+$. Moreover, we give a detailed combinatorial description of the
representation category of $D_4^+$.

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The categories of this paper are: solv-int
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th