























Abstract:We construct degeneration limits of vertex operators for the Virasoro algebra. Our method relies on the rearranged expansion of compositions of vertex operators together with their integral representations. Using this framework, we obtain a vertex operator between Verma modules of rank $r+1$ as a degeneration of a composition of two vertex operators between Verma modules of rank $r$ ($r\in\mathbb{Z}_{\geq 0}$). Furthermore, we apply these degeneration limits to prove the conjectural expansions of the $\tau$ functions of the fifth and fourth Painlevé equations in terms of irregular conformal blocks [H. Nagoya, J. Math. Phys. 56, 123505 (2015)].
From: Haruki Nakagawa [view email]
[v1]
Fri, 16 Jan 2026 09:14:25 UTC (23 KB)
[v2]
Tue, 23 Jun 2026 12:14:07 UTC (26 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。