Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the monodromy manifold of $q$-Painlev\'e VI and its Riemann-Hilbert
  problem   We study the sixth $q$-difference Painlev\'e equation
($q{\textrm{P}_{\textrm{VI}}}$) through its associated Riemann-Hilbert problem
(RHP) and show that the RHP is always solvable for irreducible monodromy data.
This enables us to identify the solution space of $q{\textrm{P}_{\textrm{VI}}}$
with a monodromy manifold for generic parameter values. We deduce this manifold
explicitly and show it is a smooth and affine algebraic surface when it does
not contain reducible monodromy. Furthermore, we describe the RHP for reducible
monodromy data and show that, when solvable, its solution is given explicitly
in terms of certain orthogonal polynomials yielding special function solutions
of $q{\textrm{P}_{\textrm{VI}}}$.

6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph