4. Polynomials and Painlevé

Problem 4.1.
Is there a relation between the polynomial roots appearing in the Painlevé equation and representation theory, for example via Young diagrams? 
Problem 4.2.
What is the precise shape of the boundary of the region containing the roots for Painlevé V? What about for the location of the zeros? 
Problem 4.3.
Consider the polynomials related to rational solutions of Painlevé equations. Are they exceptional orthogonal polynomials?
Cite this as: AimPL: Painleve equations and their applications, available at http://aimpl.org/painleveapp.