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 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.
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