Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum cluster algebras of type A and the dual canonical basis   The article concerns the subalgebra U_v^+(w) of the quantized universal
enveloping algebra of the complex Lie algebra sl_{n+1} associated with a
particular Weyl group element of length 2n. We verify that U_v^+(w) can be
endowed with the structure of a quantum cluster algebra of type A_n. The
quantum cluster algebra is a deformation of the ordinary cluster algebra
Geiss-Leclerc-Schroeer attached to w using the representation theory of the
preprojective algebra. Furthermore, we prove that the quantum cluster variables
are, up to a power of v, elements in the dual of Lusztig's canonical basis
under Kashiwara's bilinear form.

13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ