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arxiv: 1804.04782 · v2 · submitted 2018-04-13 · 🧮 math-ph · math.MP

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Remarks on irregular conformal blocks and Painlev\'e III and II tau functions

Hajime Nagoya
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classification 🧮 math-ph math.MP
keywords irregularblocksconformalfunctionsoperatorspainlevramifiedvertex
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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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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Accessory Parameter of Confluent Heun Equations, Voros Periods and classical irregular conformal blocks

    math-ph 2026-05 unverdicted novelty 6.0

    Formal series expansions of accessory parameters in confluent Heun equations are obtained from Voros periods and matched to classical irregular conformal blocks by choosing appropriate cycles on the spectral curve.