English

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

Mathematical Physics 2018-11-09 v2 math.MP

Abstract

We prove a conjecture on uniqueness and existence of the irregular vertex operators of rank rr 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.

Keywords

Cite

@article{arxiv.1804.04782,
  title  = {Remarks on irregular conformal blocks and Painlev\'e III and II tau functions},
  author = {Hajime Nagoya},
  journal= {arXiv preprint arXiv:1804.04782},
  year   = {2018}
}

Comments

13 pages, accepted to a proceeding of the workshop "Meeting for Study of Number theory, Hopf algebras and related topics", Toyama, 12-15 February 2017