Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on irregular conformal blocks and Painlev\'e III and II tau
  functions   We prove a conjecture on uniqueness and existence of the irregular vertex
operators of rank $r$ introduced in our previous paper. We also introduce
ramified irregular vertex operators of the Virasoro algebra. As applications,
we give conjectural formulas for series expansions of Painlev\'e III and II tau
functions in terms of our ramified irregular conformal blocks.

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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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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: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: dg-ga