
## 4. Polynomials and Painlevé

1. #### 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.