Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A $q$-analogue of the type $A$ Dunkl operator and integral kernel   We introduce the $q$-analogue of the type $A$ Dunkl operators, which are a
set of degree--lowering operators on the space of polynomials in $n$ variables.
This allows the construction of raising/lowering operators with a simple action
on non-symmetric Macdonald polynomials. A bilinear series of non-symmetric
Macdonald polynomials is introduced as a $q$-analogue of the type $A$ Dunkl
integral kernel ${\cal K}_A(x;y)$. The aforementioned operators are used to
show that the function satisfies $q$-analogues of the fundamental properties of
${\cal K}_A(x;y)$.

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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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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: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an