5 problems

Let $\tau_{\mathrm{I}}$ be the tau function of the first Painlevé equation, and let an irregular conformal block be a Virasoro conformal block constructed from an irregular vector.…

Let $r$ be such that the half-integer rank $r-1/2$ and the integer rank $r-1$ are defined. An irregular vector of rank $r-1/2$ is a Virasoro irregular vector associated with an irr…

An irregular vector of rank $5/2$ is a vector in a completed Virasoro Verma module associated with an irregular singularity of rank $5/2$; an irregular vector of rank $2$ is define…

Painlevé V tau-function conjecture. The function $H$ satisfies the differential equation referred to in the source as the Painlevé V Hamiltonian differential equation. This gives a…

Rank-$r$ vertex-operator existence and uniqueness conjecture. Such a vertex operator exists uniquely with the stated parameters and relations. The conjecture would provide the miss…