Abstract
| Discrete integrable systems include many types of well-known equations such as:
Hirota’s octahedron equation, the cross-ratio equation, and discrete analogues
of the Painlevé equations. One of the big questions in this area is if/how are
these systems
related to each other. Active investigations
in the past decade have led to exciting discoveries and clarifications of this
question, henceforth a better understanding
of integrable systems as a whole.
In this talk we discuss some recent progress concerning the relation between
two classes of discrete integrable systems: a list of quadrilateral equations
(known as the ABS equations) and Sakai’s classification of 22 types of discrete
Painlevé equations. This connection was made possible by exploiting
combinatorial/geometrical properties of the Weyl groups. |