Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Mirror Principle IV   This is a continuation of "Mirror Principle III"(math.AG/9912038).

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga